diff --git a/packages/components/CHANGELOG.md b/packages/components/CHANGELOG.md
index bdb1d8baa6da10..033cebd70932b4 100644
--- a/packages/components/CHANGELOG.md
+++ b/packages/components/CHANGELOG.md
@@ -5,6 +5,7 @@
 ### Bug Fix
 
 -   Replaced hardcoded blue in `ColorPicker` with UI theme color ([#36153](https://github.com/WordPress/gutenberg/pull/36153)).
+-   Fixed a bug which prevented setting `PM` hours correctly in the `DateTimePicker` ([#36878](https://github.com/WordPress/gutenberg/pull/36878)).
 
 ### Enhancements
 -   Added a `showTooltip` prop to `ToggleGroupControlOption` in order to display tooltip text (using `<Tooltip />`). ([#36726](https://github.com/WordPress/gutenberg/pull/36726)).
diff --git a/packages/components/src/date-time/test/time.js b/packages/components/src/date-time/test/time.js
index 7124e80e6c1b1a..523f2447e6acf2 100644
--- a/packages/components/src/date-time/test/time.js
+++ b/packages/components/src/date-time/test/time.js
@@ -47,13 +47,13 @@ describe( 'TimePicker', () => {
 		fireEvent.change( hoursInput, { target: { value: '12' } } );
 		fireEvent.blur( hoursInput );
 
-		expect( onChangeSpy ).toHaveBeenCalledWith( '2018-12-22T12:00:00' );
+		expect( onChangeSpy ).toHaveBeenCalledWith( '2018-12-22T00:00:00' );
 		onChangeSpy.mockClear();
 
 		fireEvent.change( minutesInput, { target: { value: '35' } } );
 		fireEvent.blur( minutesInput );
 
-		expect( onChangeSpy ).toHaveBeenCalledWith( '2018-12-22T12:35:00' );
+		expect( onChangeSpy ).toHaveBeenCalledWith( '2018-12-22T00:35:00' );
 		onChangeSpy.mockClear();
 	} );
 
@@ -169,6 +169,36 @@ describe( 'TimePicker', () => {
 		expect( onChangeSpy ).toHaveBeenCalledWith( '1986-10-18T11:00:00' );
 	} );
 
+	it( 'should allow to set the time correctly when the PM period is selected', () => {
+		const onChangeSpy = jest.fn();
+
+		render(
+			<TimePicker
+				currentTime="1986-10-18T11:00:00"
+				onChange={ onChangeSpy }
+				is12Hour
+			/>
+		);
+
+		const pmButton = screen.getByText( 'PM' );
+		fireEvent.click( pmButton );
+
+		const hoursInput = screen.getByLabelText( 'Hours' );
+		fireEvent.change( hoursInput, { target: { value: '6' } } );
+		fireEvent.blur( hoursInput );
+
+		// When clicking on 'PM', we expect the time to be 11pm
+		expect( onChangeSpy ).toHaveBeenNthCalledWith(
+			1,
+			'1986-10-18T23:00:00'
+		);
+		// When changing the hours to '6', we expect the time to be 6pm
+		expect( onChangeSpy ).toHaveBeenNthCalledWith(
+			2,
+			'1986-10-18T18:00:00'
+		);
+	} );
+
 	it( 'should truncate at the minutes on change', () => {
 		const onChangeSpy = jest.fn();
 
diff --git a/packages/components/src/date-time/time.js b/packages/components/src/date-time/time.js
index 9063a6011a3357..098fba0d9cfabc 100644
--- a/packages/components/src/date-time/time.js
+++ b/packages/components/src/date-time/time.js
@@ -28,6 +28,10 @@ import TimeZone from './timezone';
  */
 const TIMEZONELESS_FORMAT = 'YYYY-MM-DDTHH:mm:ss';
 
+function from12hTo24h( hours, isPm ) {
+	return isPm ? ( ( hours % 12 ) + 12 ) % 24 : hours % 12;
+}
+
 /**
  * <UpdateOnBlurAsIntegerField>
  * A shared component to parse, validate, and handle remounting of the underlying form field element like <input> and <select>.
@@ -117,8 +121,16 @@ export function TimePicker( { is12Hour, currentTime, onChange } ) {
 	}
 
 	function update( name, value ) {
+		// If the 12-hour format is being used and the 'PM' period is selected, then
+		// the incoming value (which ranges 1-12) should be increased by 12 to match
+		// the expected 24-hour format.
+		let adjustedValue = value;
+		if ( name === 'hours' && is12Hour ) {
+			adjustedValue = from12hTo24h( value, am === 'PM' );
+		}
+
 		// Clone the date and call the specific setter function according to `name`.
-		const newDate = date.clone()[ name ]( value );
+		const newDate = date.clone()[ name ]( adjustedValue );
 		changeDate( newDate );
 	}
 
@@ -132,11 +144,7 @@ export function TimePicker( { is12Hour, currentTime, onChange } ) {
 
 			const newDate = date
 				.clone()
-				.hours(
-					value === 'PM'
-						? ( ( parsedHours % 12 ) + 12 ) % 24
-						: parsedHours % 12
-				);
+				.hours( from12hTo24h( parsedHours, value === 'PM' ) );
 
 			changeDate( newDate );
 		};