The couple posed for their first picture together after the announcement on Monday.
Asked if his proposal was romantic, Harry replied: "Of course it was," before leaving with an arm around his fiancée who showed off her diamond engagement ring to photographers.
Harry, 33, Queen Elizabeth's grandson and fifth in line to the British throne, and Markle, 36, best known for her role in the US TV legal drama Suits, got engaged earlier this month in London.