The fifth in line to the throne will marry Ms Markle in spring 2018.
The couple, who have been dating since the summer of 2016, smiled as they posed for photographs outside Kensington Palace in London, where they will live.
Prince Harry said it had been a romantic proposal, while Ms Markle said she was “so very happy, thank you”.
Ms Markle, wearing a white belted coat, held Harry’s hand as they appeared briefly for the press at the palace’s Sunken Garden, and showed off her diamond engagement ring.
Asked by a reporter when he knew Suits star Ms Markle “was the one”, Prince Harry said: “The very first time we met”.
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