diff --git a/src/cdk/stepper/stepper.ts b/src/cdk/stepper/stepper.ts
index 8fec6f00156c..4f1232786eb9 100644
--- a/src/cdk/stepper/stepper.ts
+++ b/src/cdk/stepper/stepper.ts
@@ -321,6 +321,9 @@ export class CdkStepper implements AfterContentInit, AfterViewInit, OnDestroy {
   /** Event emitted when the selected step has changed. */
   @Output() readonly selectionChange = new EventEmitter<StepperSelectionEvent>();
 
+  /** Output to support two-way binding on `[(selectedIndex)]` */
+  @Output() readonly selectedIndexChange: EventEmitter<number> = new EventEmitter<number>();
+
   /** Used to track unique ID for each stepper component. */
   _groupId: number;
 
@@ -526,6 +529,7 @@ export class CdkStepper implements AfterContentInit, AfterViewInit, OnDestroy {
       : this._keyManager.updateActiveItem(newIndex);
 
     this._selectedIndex = newIndex;
+    this.selectedIndexChange.emit(this._selectedIndex);
     this._stateChanged();
   }
 
diff --git a/src/material/stepper/stepper.spec.ts b/src/material/stepper/stepper.spec.ts
index 3f50fc20af6c..ac8fcefb6a69 100644
--- a/src/material/stepper/stepper.spec.ts
+++ b/src/material/stepper/stepper.spec.ts
@@ -1571,6 +1571,35 @@ describe('MatStepper', () => {
       expect(element.textContent).toContain('Step 3 content');
     });
   });
+
+  describe('stepper with two-way binding on selectedIndex', () => {
+    it('should update selectedIndex in component on navigation', () => {
+      const fixture = createComponent(StepperWithTwoWayBindingOnSelectedIndex);
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.index).toBe(0);
+
+      const stepHeaders = fixture.debugElement.queryAll(By.css('.mat-horizontal-stepper-header'));
+
+      let lastStepHeaderEl = stepHeaders[2].nativeElement;
+      lastStepHeaderEl.click();
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.index).toBe(2);
+
+      let middleStepHeaderEl = stepHeaders[1].nativeElement;
+      middleStepHeaderEl.click();
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.index).toBe(1);
+
+      let firstStepHeaderEl = stepHeaders[0].nativeElement;
+      firstStepHeaderEl.click();
+      fixture.detectChanges();
+
+      expect(fixture.componentInstance.index).toBe(0);
+    });
+  });
 });
 
 /** Asserts that keyboard interaction works correctly. */
@@ -2166,3 +2195,16 @@ class StepperWithLazyContent {
 class HorizontalStepperWithDelayedStep {
   renderSecondStep = false;
 }
+
+@Component({
+  template: `
+    <mat-stepper [(selectedIndex)]="index">
+      <mat-step label="One"></mat-step>
+      <mat-step label="Two"></mat-step>
+      <mat-step label="Three"></mat-step>
+    </mat-stepper>
+  `,
+})
+class StepperWithTwoWayBindingOnSelectedIndex {
+  index: number = 0;
+}
diff --git a/tools/public_api_guard/cdk/stepper.md b/tools/public_api_guard/cdk/stepper.md
index c7c659bebfc5..a7e966b0f452 100644
--- a/tools/public_api_guard/cdk/stepper.md
+++ b/tools/public_api_guard/cdk/stepper.md
@@ -115,13 +115,14 @@ export class CdkStepper implements AfterContentInit, AfterViewInit, OnDestroy {
     set selected(step: CdkStep | undefined);
     get selectedIndex(): number;
     set selectedIndex(index: NumberInput);
+    readonly selectedIndexChange: EventEmitter<number>;
     readonly selectionChange: EventEmitter<StepperSelectionEvent>;
     _stateChanged(): void;
     _stepHeader: QueryList<CdkStepHeader>;
     readonly steps: QueryList<CdkStep>;
     _steps: QueryList<CdkStep>;
     // (undocumented)
-    static ɵdir: i0.ɵɵDirectiveDeclaration<CdkStepper, "[cdkStepper]", ["cdkStepper"], { "linear": { "alias": "linear"; "required": false; }; "selectedIndex": { "alias": "selectedIndex"; "required": false; }; "selected": { "alias": "selected"; "required": false; }; "orientation": { "alias": "orientation"; "required": false; }; }, { "selectionChange": "selectionChange"; }, ["_steps", "_stepHeader"], never, false, never, false>;
+    static ɵdir: i0.ɵɵDirectiveDeclaration<CdkStepper, "[cdkStepper]", ["cdkStepper"], { "linear": { "alias": "linear"; "required": false; }; "selectedIndex": { "alias": "selectedIndex"; "required": false; }; "selected": { "alias": "selected"; "required": false; }; "orientation": { "alias": "orientation"; "required": false; }; }, { "selectionChange": "selectionChange"; "selectedIndexChange": "selectedIndexChange"; }, ["_steps", "_stepHeader"], never, false, never, false>;
     // (undocumented)
     static ɵfac: i0.ɵɵFactoryDeclaration<CdkStepper, [{ optional: true; }, null, null]>;
 }