diff --git a/src/app/core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-move-operation.model.ts b/src/app/core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-move-operation.model.ts
new file mode 100644
index 0000000000..962d53dfee
--- /dev/null
+++ b/src/app/core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-move-operation.model.ts
@@ -0,0 +1,33 @@
+import { MetadataPatchOperation } from './metadata-patch-operation.model';
+import { Operation } from 'fast-json-patch';
+
+/**
+ * Wrapper object for a metadata patch move Operation
+ */
+export class MetadataPatchMoveOperation extends MetadataPatchOperation {
+  static operationType = 'move';
+
+  /**
+   * The original place of the metadata value to move
+   */
+  from: number;
+
+  /**
+   * The new place to move the metadata value to
+   */
+  to: number;
+
+  constructor(field: string, from: number, to: number) {
+    super(MetadataPatchMoveOperation.operationType, field);
+    this.from = from;
+    this.to = to;
+  }
+
+  /**
+   * Transform the MetadataPatchOperation into a fast-json-patch Operation by constructing its path and other properties
+   * using the information provided.
+   */
+  toOperation(): Operation {
+    return { op: this.op as any, from: `/metadata/${this.field}/${this.from}`, path: `/metadata/${this.field}/${this.to}` };
+  }
+}
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.html b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.html
index 6a0386da8e..190d5a7e31 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.html
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.html
@@ -1,4 +1,4 @@
-<div class="flex-grow-1 ds-drop-list h-100">
+<div class="flex-grow-1 ds-drop-list h-100" [class.disabled]="(draggingMdField$ | async) && (draggingMdField$ | async) !== mdField" cdkDropList (cdkDropListDropped)="drop($event)">
   <ds-dso-edit-metadata-value *ngFor="let mdValue of form.fields[mdField]; let idx = index"
                               [dso]="dso"
                               [mdValue]="mdValue"
@@ -8,6 +8,7 @@
                               (edit)="mdValue.editing = true"
                               (confirm)="mdValue.confirmChanges($event); form.resetReinstatable(); valueSaved.emit()"
                               (remove)="mdValue.change = DsoEditMetadataChangeTypeEnum.REMOVE; form.resetReinstatable(); valueSaved.emit()"
-                              (undo)="mdValue.change === DsoEditMetadataChangeTypeEnum.ADD ? form.remove(mdField, idx) : mdValue.discard(); valueSaved.emit()">
+                              (undo)="mdValue.change === DsoEditMetadataChangeTypeEnum.ADD ? form.remove(mdField, idx) : mdValue.discard(); valueSaved.emit()"
+                              (dragging)="$event ? draggingMdField$.next(mdField) : draggingMdField$.next(null)">
   </ds-dso-edit-metadata-value>
 </div>
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.scss b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.scss
index afe5084bc2..6b52c4f4b3 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.scss
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.scss
@@ -1,3 +1,7 @@
 .ds-drop-list {
   background-color: var(--bs-gray-500);
+
+  &.disabled {
+    opacity: 0.3;
+  }
 }
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.ts b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.ts
index 0db427c218..2702e0ba1f 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.ts
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-field-values/dso-edit-metadata-field-values.component.ts
@@ -1,7 +1,9 @@
 import { Component, EventEmitter, Input, Output } from '@angular/core';
-import { DsoEditMetadataChangeType, DsoEditMetadataForm } from '../dso-edit-metadata-form';
+import { DsoEditMetadataChangeType, DsoEditMetadataForm, DsoEditMetadataValue } from '../dso-edit-metadata-form';
 import { Observable } from 'rxjs/internal/Observable';
 import { DSpaceObject } from '../../../core/shared/dspace-object.model';
+import { BehaviorSubject } from 'rxjs/internal/BehaviorSubject';
+import { CdkDragDrop, moveItemInArray } from '@angular/cdk/drag-drop';
 
 @Component({
   selector: 'ds-dso-edit-metadata-field-values',
@@ -38,6 +40,12 @@ export class DsoEditMetadataFieldValuesComponent {
    */
   @Input() saving$: Observable<boolean>;
 
+  /**
+   * Tracks for which metadata-field a drag operation is taking place
+   * Null when no drag is currently happening for any field
+   */
+  @Input() draggingMdField$: BehaviorSubject<string>;
+
   /**
    * Emit when the value has been saved within the form
    */
@@ -48,4 +56,26 @@ export class DsoEditMetadataFieldValuesComponent {
    * @type {DsoEditMetadataChangeType}
    */
   public DsoEditMetadataChangeTypeEnum = DsoEditMetadataChangeType;
+
+  /**
+   * Drop a value into a new position
+   * Update the form's value array for the current field to match the dropped position
+   * Update the values their place property to match the new order
+   * Send an update to the parent
+   * @param event
+   */
+  drop(event: CdkDragDrop<any>) {
+    const dragIndex = event.previousIndex;
+    const dropIndex = event.currentIndex;
+    // Move the value within its field
+    moveItemInArray(this.form.fields[this.mdField], dragIndex, dropIndex);
+    // Update all the values in this field their place property
+    this.form.fields[this.mdField].forEach((value: DsoEditMetadataValue, index: number) => {
+      value.newValue.place = index;
+      value.confirmChanges();
+    });
+    // Update the form statuses
+    this.form.resetReinstatable();
+    this.valueSaved.emit();
+  }
 }
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-form.ts b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-form.ts
index fde0ecf9d4..cc1f55838b 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-form.ts
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-form.ts
@@ -1,10 +1,11 @@
 import { MetadataMap, MetadataValue } from '../../core/shared/metadata.models';
 import { hasNoValue, hasValue, isEmpty, isNotEmpty } from '../../shared/empty.util';
-import { Operation } from 'fast-json-patch';
+import { MoveOperation, Operation } from 'fast-json-patch';
 import { MetadataPatchReplaceOperation } from '../../core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-replace-operation.model';
 import { MetadataPatchRemoveOperation } from '../../core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-remove-operation.model';
 import { MetadataPatchAddOperation } from '../../core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-add-operation.model';
-import { MetadataPatchOperation } from '../../core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-operation.model';
+import { ArrayMoveChangeAnalyzer } from '../../core/data/array-move-change-analyzer.service';
+import { MetadataPatchMoveOperation } from '../../core/data/object-updates/patch-operation-service/operations/metadata/metadata-patch-move-operation.model';
 
 /* tslint:disable:max-classes-per-file */
 
@@ -69,7 +70,7 @@ export class DsoEditMetadataValue {
    */
   confirmChanges(finishEditing = false) {
     if (hasNoValue(this.change) || this.change === DsoEditMetadataChangeType.UPDATE) {
-      if ((this.originalValue.value !== this.newValue.value || this.originalValue.language !== this.newValue.language)) {
+      if ((this.originalValue.value !== this.newValue.value || this.originalValue.language !== this.newValue.language || this.originalValue.place !== this.newValue.place)) {
         this.change = DsoEditMetadataChangeType.UPDATE;
       } else {
         this.change = undefined;
@@ -187,7 +188,7 @@ export class DsoEditMetadataForm {
     Object.entries(metadata).forEach(([mdField, values]: [string, MetadataValue[]]) => {
       this.originalFieldKeys.push(mdField);
       this.fieldKeys.push(mdField);
-      this.fields[mdField] = values.map((value: MetadataValue) => new DsoEditMetadataValue(value));
+      this.setValuesForFieldSorted(mdField, values.map((value: MetadataValue) => new DsoEditMetadataValue(value)));
     });
   }
 
@@ -208,6 +209,10 @@ export class DsoEditMetadataForm {
   setMetadataField(mdField: string): void {
     this.newValue.editing = false;
     this.addValueToField(this.newValue, mdField);
+    // Set the place property to match the new value's position within its field
+    const place = this.fields[mdField].length - 1;
+    this.fields[mdField][place].originalValue.place = place;
+    this.fields[mdField][place].newValue.place = place;
     this.newValue = undefined;
   }
 
@@ -253,6 +258,7 @@ export class DsoEditMetadataForm {
    */
   discard(): void {
     this.resetReinstatable();
+    // Discard changes from each value from each field
     Object.entries(this.fields).forEach(([field, values]: [string, DsoEditMetadataValue[]]) => {
       let removeFromIndex = -1;
       values.forEach((value: DsoEditMetadataValue, index: number) => {
@@ -272,25 +278,39 @@ export class DsoEditMetadataForm {
         this.fields[field].splice(removeFromIndex, this.fields[field].length - removeFromIndex);
       }
     });
+    // Delete new metadata fields
     this.fieldKeys.forEach((field: string) => {
       if (this.originalFieldKeys.indexOf(field) < 0) {
         delete this.fields[field];
       }
     });
     this.fieldKeys = [...this.originalFieldKeys];
+    // Reset the order of values within their fields to match their place property
+    this.fieldKeys.forEach((field: string) => {
+      this.setValuesForFieldSorted(field, this.fields[field]);
+    });
   }
 
+  /**
+   * Undo any previously discarded changes
+   */
   reinstate(): void {
+    // Reinstate each value
     Object.values(this.fields).forEach((values: DsoEditMetadataValue[]) => {
       values.forEach((value: DsoEditMetadataValue) => {
         value.reinstate();
       });
     });
+    // Re-add new values
     Object.entries(this.reinstatableNewValues).forEach(([field, values]: [string, DsoEditMetadataValue[]]) => {
       values.forEach((value: DsoEditMetadataValue) => {
         this.addValueToField(value, field);
       });
     });
+    // Reset the order of values within their fields to match their place property
+    this.fieldKeys.forEach((field: string) => {
+      this.setValuesForFieldSorted(field, this.fields[field]);
+    });
     this.reinstatableNewValues = {};
   }
 
@@ -317,34 +337,73 @@ export class DsoEditMetadataForm {
   }
 
   /**
-   * Get the json PATCH operations for the current changes within this form
+   * Set the values of a metadata field and sort them by their newValue's place property
+   * @param mdField
+   * @param values
    */
-  getOperations(): Operation[] {
+  private setValuesForFieldSorted(mdField: string, values: DsoEditMetadataValue[]) {
+    this.fields[mdField] = values.sort((a: DsoEditMetadataValue, b: DsoEditMetadataValue) => a.newValue.place - b.newValue.place);
+  }
+
+  /**
+   * Get the json PATCH operations for the current changes within this form
+   * For each metadata field, it'll return operations in the following order: replace, remove (from last to first place), add and move
+   * This order is important, as each operation is executed in succession of the previous one
+   */
+  getOperations(moveAnalyser: ArrayMoveChangeAnalyzer<number>): Operation[] {
     const operations: Operation[] = [];
     Object.entries(this.fields).forEach(([field, values]: [string, DsoEditMetadataValue[]]) => {
-      values.forEach((value: DsoEditMetadataValue, place: number) => {
-        if (value.hasChanges()) {
-          let operation: MetadataPatchOperation;
-          if (value.change === DsoEditMetadataChangeType.UPDATE) {
-            operation = new MetadataPatchReplaceOperation(field, place, {
-              value: value.newValue.value,
-              language: value.newValue.language,
-            });
-          } else if (value.change === DsoEditMetadataChangeType.REMOVE) {
-            operation = new MetadataPatchRemoveOperation(field, place);
-          } else if (value.change === DsoEditMetadataChangeType.ADD) {
-            operation = new MetadataPatchAddOperation(field, {
-              value: value.newValue.value,
-              language: value.newValue.language,
-            });
-          } else {
-            console.warn('Illegal metadata change state detected for', value);
+      const replaceOperations: MetadataPatchReplaceOperation[] = [];
+      const removeOperations: MetadataPatchRemoveOperation[] = [];
+      const addOperations: MetadataPatchAddOperation[] = [];
+      values
+        .sort((a: DsoEditMetadataValue, b: DsoEditMetadataValue) => a.originalValue.place - b.originalValue.place)
+        .forEach((value: DsoEditMetadataValue) => {
+          if (value.hasChanges()) {
+            if (value.change === DsoEditMetadataChangeType.UPDATE) {
+              // Only changes to value or language are considered "replace" operations. Changes to place are considered "move", which is processed below.
+              if (value.originalValue.value !== value.newValue.value || value.originalValue.language !== value.newValue.language) {
+                replaceOperations.push(new MetadataPatchReplaceOperation(field, value.originalValue.place, {
+                  value: value.newValue.value,
+                  language: value.newValue.language,
+                }));
+              }
+            } else if (value.change === DsoEditMetadataChangeType.REMOVE) {
+              removeOperations.push(new MetadataPatchRemoveOperation(field, value.originalValue.place));
+            } else if (value.change === DsoEditMetadataChangeType.ADD) {
+              addOperations.push(new MetadataPatchAddOperation(field, {
+                value: value.newValue.value,
+                language: value.newValue.language,
+              }));
+            } else {
+              console.warn('Illegal metadata change state detected for', value);
+            }
           }
-          if (hasValue(operation)) {
-            operations.push(operation.toOperation());
-          }
-        }
-      });
+        });
+
+      operations.push(...replaceOperations
+        .map((operation: MetadataPatchReplaceOperation) => operation.toOperation()));
+      operations.push(...removeOperations
+        // Sort remove operations backwards first, because they get executed in order. This avoids one removal affecting the next.
+        .sort((a: MetadataPatchRemoveOperation, b: MetadataPatchRemoveOperation) => b.place - a.place)
+        .map((operation: MetadataPatchRemoveOperation) => operation.toOperation()));
+      operations.push(...addOperations
+        .map((operation: MetadataPatchAddOperation) => operation.toOperation()));
+    });
+    // Calculate and add the move operations that need to happen in order to move value from their old place to their new within the field
+    // This uses an ArrayMoveChangeAnalyzer
+    Object.entries(this.fields).forEach(([field, values]: [string, DsoEditMetadataValue[]]) => {
+      // Exclude values marked for removal, because operations are executed in order (remove first, then move)
+      const valuesWithoutRemoved = values.filter((value: DsoEditMetadataValue) => value.change !== DsoEditMetadataChangeType.REMOVE);
+      const moveOperations = moveAnalyser
+        .diff(
+          valuesWithoutRemoved
+            .map((value: DsoEditMetadataValue) => value.originalValue.place),
+          valuesWithoutRemoved
+            .sort((a: DsoEditMetadataValue, b: DsoEditMetadataValue) => a.newValue.place - b.newValue.place)
+            .map((value: DsoEditMetadataValue) => value.originalValue.place))
+        .map((operation: MoveOperation) => new MetadataPatchMoveOperation(field, +operation.from.substr(1), +operation.path.substr(1)).toOperation());
+      operations.push(...moveOperations);
     });
     return operations;
   }
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.html b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.html
index e72a9e8444..9941d03308 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.html
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.html
@@ -1,4 +1,5 @@
 <div class="d-flex flex-row ds-value-row" *ngVar="mdValue.newValue.isVirtual as isVirtual"
+     cdkDrag (cdkDragStarted)="dragging.emit(true)" (cdkDragEnded)="dragging.emit(false)"
      [ngClass]="{ 'ds-warning': mdValue.change === DsoEditMetadataChangeTypeEnum.UPDATE, 'ds-danger': mdValue.change === DsoEditMetadataChangeTypeEnum.REMOVE, 'ds-success': mdValue.change === DsoEditMetadataChangeTypeEnum.ADD, 'h-100': isOnlyValue }">
   <div class="flex-grow-1 ds-flex-cell ds-value-cell d-flex align-items-center" *ngVar="(mdRepresentation$ | async) as mdRepresentation">
     <div class="dont-break-out preserve-line-breaks" *ngIf="!mdValue.editing && !mdRepresentation">{{ mdValue.newValue.value }}</div>
@@ -34,8 +35,7 @@
           <i class="fas fa-undo-alt fa-fw"></i>
         </button>
       </div>
-      <!-- TODO: Enable drag -->
-      <button class="btn btn-outline-secondary ds-drag-handle btn-sm"
+      <button class="btn btn-outline-secondary ds-drag-handle btn-sm" cdkDragHandle
               [ngClass]="{'disabled': isOnlyValue || (saving$ | async)}" ngbTooltip="{{ dsoType + '.edit.metadata.edit.buttons.drag' | translate }}" [disabled]="isOnlyValue || (saving$ | async)">
         <i class="fas fa-grip-vertical fa-fw"></i>
       </button>
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.scss b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.scss
index 1196aa1940..bcf491b9ce 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.scss
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.scss
@@ -10,3 +10,7 @@
 ::ng-deep .tooltip-inner {
   min-width: var(--ds-dso-edit-virtual-tooltip-min-width);
 }
+
+.cdk-drag-placeholder {
+  opacity: 0;
+}
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.ts b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.ts
index b61255e4fe..dce0ec68b0 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.ts
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata-value/dso-edit-metadata-value.component.ts
@@ -71,6 +71,11 @@ export class DsoEditMetadataValueComponent implements OnInit {
    */
   @Output() undo: EventEmitter<any> = new EventEmitter<any>();
 
+  /**
+   * Emits true when the user starts dragging a value, false when the user stops dragging
+   */
+  @Output() dragging: EventEmitter<boolean> = new EventEmitter<boolean>();
+
   /**
    * The DsoEditMetadataChangeType enumeration for access in the component's template
    * @type {DsoEditMetadataChangeType}
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.html b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.html
index 0ca62ff1b6..e498dc373e 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.html
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.html
@@ -48,6 +48,7 @@
                                        [form]="form"
                                        [dsoType]="dsoType"
                                        [saving$]="saving$"
+                                       [draggingMdField$]="draggingMdField$"
                                        [mdField]="mdField"
                                        (valueSaved)="onValueSaved()">
     </ds-dso-edit-metadata-field-values>
diff --git a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.ts b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.ts
index e98cc3663d..7f98720b2c 100644
--- a/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.ts
+++ b/src/app/dso-shared/dso-edit-metadata/dso-edit-metadata.component.ts
@@ -19,6 +19,7 @@ import { NotificationsService } from '../../shared/notifications/notifications.s
 import { TranslateService } from '@ngx-translate/core';
 import { MetadataFieldSelectorComponent } from './metadata-field-selector/metadata-field-selector.component';
 import { Observable } from 'rxjs/internal/Observable';
+import { ArrayMoveChangeAnalyzer } from '../../core/data/array-move-change-analyzer.service';
 
 @Component({
   selector: 'ds-dso-edit-metadata',
@@ -72,6 +73,13 @@ export class DsoEditMetadataComponent implements OnInit, OnDestroy {
    */
   saving$: BehaviorSubject<boolean> = new BehaviorSubject<boolean>(false);
 
+  /**
+   * Tracks for which metadata-field a drag operation is taking place
+   * Null when no drag is currently happening for any field
+   * This is a BehaviorSubject that is passed down to child components, to give them the power to alter the state
+   */
+  draggingMdField$: BehaviorSubject<string> = new BehaviorSubject<string>(null);
+
   /**
    * Whether or not the metadata field is currently being validated
    */
@@ -98,7 +106,8 @@ export class DsoEditMetadataComponent implements OnInit, OnDestroy {
   constructor(protected route: ActivatedRoute,
               protected notificationsService: NotificationsService,
               protected translateService: TranslateService,
-              protected parentInjector: Injector) {
+              protected parentInjector: Injector,
+              protected arrayMoveChangeAnalyser: ArrayMoveChangeAnalyzer<number>) {
   }
 
   /**
@@ -167,7 +176,7 @@ export class DsoEditMetadataComponent implements OnInit, OnDestroy {
    */
   submit(): void {
     this.saving$.next(true);
-    this.updateDataService.patch(this.dso, this.form.getOperations()).pipe(
+    this.updateDataService.patch(this.dso, this.form.getOperations(this.arrayMoveChangeAnalyser)).pipe(
       getFirstCompletedRemoteData()
     ).subscribe((rd: RemoteData<DSpaceObject>) => {
       this.saving$.next(false);