diff --git a/src/material/tooltip/tooltip.spec.ts b/src/material/tooltip/tooltip.spec.ts
index 06f887ef99ca..2f6382906c02 100644
--- a/src/material/tooltip/tooltip.spec.ts
+++ b/src/material/tooltip/tooltip.spec.ts
@@ -111,17 +111,17 @@ describe('MatTooltip', () => {
 
       fixture.detectChanges();
 
-      // wait till animation has finished
+      // Wait until the animation has finished.
       tick(500);
 
-      // Make sure tooltip is shown to the user and animation has finished
+      // Make sure tooltip is shown to the user and animation has finished.
       const tooltipElement = overlayContainerElement.querySelector('.mat-tooltip') as HTMLElement;
       expect(tooltipElement instanceof HTMLElement).toBe(true);
       expect(tooltipElement.style.transform).toBe('scale(1)');
 
       expect(overlayContainerElement.textContent).toContain(initialTooltipMessage);
 
-      // After hide called, a timeout delay is created that will to hide the tooltip.
+      // After hide is called, a timeout delay is created that will to hide the tooltip.
       const tooltipDelay = 1000;
       tooltipDirective.hide(tooltipDelay);
       expect(tooltipDirective._isTooltipVisible()).toBe(true);
@@ -719,6 +719,33 @@ describe('MatTooltip', () => {
       expect(overlayRef.detach).not.toHaveBeenCalled();
     }));
 
+    it('should clear the show timeout on destroy', fakeAsync(() => {
+      assertTooltipInstance(tooltipDirective, false);
+
+      tooltipDirective.show(1000);
+      fixture.detectChanges();
+
+      // Note that we aren't asserting anything, but `fakeAsync` will
+      // throw if we have any timers by the end of the test.
+      fixture.destroy();
+    }));
+
+    it('should clear the hide timeout on destroy', fakeAsync(() => {
+      assertTooltipInstance(tooltipDirective, false);
+
+      tooltipDirective.show();
+      tick(0);
+      fixture.detectChanges();
+      tick(500);
+
+      tooltipDirective.hide(1000);
+      fixture.detectChanges();
+
+      // Note that we aren't asserting anything, but `fakeAsync` will
+      // throw if we have any timers by the end of the test.
+      fixture.destroy();
+    }));
+
   });
 
   describe('fallback positions', () => {
diff --git a/src/material/tooltip/tooltip.ts b/src/material/tooltip/tooltip.ts
index 040cdaf2d233..5d82adbe7180 100644
--- a/src/material/tooltip/tooltip.ts
+++ b/src/material/tooltip/tooltip.ts
@@ -550,10 +550,10 @@ export class TooltipComponent implements OnDestroy {
   tooltipClass: string|string[]|Set<string>|{[key: string]: any};
 
   /** The timeout ID of any current timer set to show the tooltip */
-  _showTimeoutId: number | null;
+  _showTimeoutId: number | undefined;
 
   /** The timeout ID of any current timer set to hide the tooltip */
-  _hideTimeoutId: number | null;
+  _hideTimeoutId: number | undefined;
 
   /** Property watched by the animation framework to show or hide the tooltip */
   _visibility: TooltipVisibility = 'initial';
@@ -577,16 +577,13 @@ export class TooltipComponent implements OnDestroy {
    */
   show(delay: number): void {
     // Cancel the delayed hide if it is scheduled
-    if (this._hideTimeoutId) {
-      clearTimeout(this._hideTimeoutId);
-      this._hideTimeoutId = null;
-    }
+    clearTimeout(this._hideTimeoutId);
 
     // Body interactions should cancel the tooltip if there is a delay in showing.
     this._closeOnInteraction = true;
     this._showTimeoutId = setTimeout(() => {
       this._visibility = 'visible';
-      this._showTimeoutId = null;
+      this._showTimeoutId = undefined;
 
       // Mark for check so if any parent component has set the
       // ChangeDetectionStrategy to OnPush it will be checked anyways
@@ -600,14 +597,11 @@ export class TooltipComponent implements OnDestroy {
    */
   hide(delay: number): void {
     // Cancel the delayed show if it is scheduled
-    if (this._showTimeoutId) {
-      clearTimeout(this._showTimeoutId);
-      this._showTimeoutId = null;
-    }
+    clearTimeout(this._showTimeoutId);
 
     this._hideTimeoutId = setTimeout(() => {
       this._visibility = 'hidden';
-      this._hideTimeoutId = null;
+      this._hideTimeoutId = undefined;
 
       // Mark for check so if any parent component has set the
       // ChangeDetectionStrategy to OnPush it will be checked anyways
@@ -626,6 +620,8 @@ export class TooltipComponent implements OnDestroy {
   }
 
   ngOnDestroy() {
+    clearTimeout(this._showTimeoutId);
+    clearTimeout(this._hideTimeoutId);
     this._onHide.complete();
   }
 
diff --git a/tools/public_api_guard/material/tooltip.d.ts b/tools/public_api_guard/material/tooltip.d.ts
index 849be20c555b..c169bdd6b3c2 100644
--- a/tools/public_api_guard/material/tooltip.d.ts
+++ b/tools/public_api_guard/material/tooltip.d.ts
@@ -63,9 +63,9 @@ export declare const SCROLL_THROTTLE_MS = 20;
 export declare const TOOLTIP_PANEL_CLASS = "mat-tooltip-panel";
 
 export declare class TooltipComponent implements OnDestroy {
-    _hideTimeoutId: number | null;
+    _hideTimeoutId: number | undefined;
     _isHandset: Observable<BreakpointState>;
-    _showTimeoutId: number | null;
+    _showTimeoutId: number | undefined;
     _visibility: TooltipVisibility;
     message: string;
     tooltipClass: string | string[] | Set<string> | {