diff --git a/packages/components/src/tooltip/test/index.tsx b/packages/components/src/tooltip/test/index.tsx
index 67922ab1d5ac4..3679b597b2cb1 100644
--- a/packages/components/src/tooltip/test/index.tsx
+++ b/packages/components/src/tooltip/test/index.tsx
@@ -516,4 +516,82 @@ describe( 'Tooltip', () => {
 			).not.toHaveClass( 'components-tooltip' );
 		} );
 	} );
+
+	describe( 'aria-describedby', () => {
+		it( "should not override the anchor's aria-describedby attribute if specified", async () => {
+			render(
+				<>
+					<Tooltip { ...props }>
+						<button aria-describedby="tooltip-test-description">
+							Tooltip anchor
+						</button>
+					</Tooltip>
+					{ /* eslint-disable-next-line no-restricted-syntax */ }
+					<p id="tooltip-test-description">Tooltip description</p>
+					<button>focus trap outside</button>
+				</>
+			);
+
+			expect(
+				screen.getByRole( 'button', { name: 'Tooltip anchor' } )
+			).toHaveAccessibleDescription( 'Tooltip description' );
+
+			// Focus the anchor, tooltip should show
+			await press.Tab();
+			expect(
+				screen.getByRole( 'button', { name: 'Tooltip anchor' } )
+			).toHaveFocus();
+			await waitExpectTooltipToShow();
+
+			// The anchors should retain its previous accessible description,
+			// since the tooltip shouldn't override it.
+			expect(
+				screen.getByRole( 'button', { name: 'Tooltip anchor' } )
+			).toHaveAccessibleDescription( 'Tooltip description' );
+
+			// Focus the other button, tooltip should hide
+			await press.Tab();
+			expect(
+				screen.getByRole( 'button', { name: 'focus trap outside' } )
+			).toHaveFocus();
+			await waitExpectTooltipToHide();
+		} );
+
+		it( "should not add the aria-describedby attribute to the anchor if the tooltip text matches the anchor's aria-label", async () => {
+			render(
+				<>
+					<Tooltip { ...props }>
+						<button aria-label={ props.text }>
+							Tooltip anchor
+						</button>
+					</Tooltip>
+					<button>focus trap outside</button>
+				</>
+			);
+
+			expect(
+				screen.getByRole( 'button', { name: props.text } )
+			).not.toHaveAccessibleDescription();
+
+			// Focus the anchor, tooltip should show
+			await press.Tab();
+			expect(
+				screen.getByRole( 'button', { name: props.text } )
+			).toHaveFocus();
+			await waitExpectTooltipToShow();
+
+			// The anchor shouldn't have an aria-describedby prop
+			// because its aria-label matches the tooltip text.
+			expect(
+				screen.getByRole( 'button', { name: props.text } )
+			).not.toHaveAccessibleDescription();
+
+			// Focus the other button, tooltip should hide
+			await press.Tab();
+			expect(
+				screen.getByRole( 'button', { name: 'focus trap outside' } )
+			).toHaveFocus();
+			await waitExpectTooltipToHide();
+		} );
+	} );
 } );