The Queen's grandson declared himself to be "thrilled" and "over the moon" to be engaged to the American actress after a whirlwind romance lasting just 16 months.
The happy couple made their first appearance in public since the announcement of their impending nuptials, posing for photographs in the Sunken Garden at Kensington Palace.
Ms Markle showed off her sparkling engagement ring, which romantic Harry designed himself, made from two diamonds which belonged to his late beloved mother Diana, Princess of Wales.
The ring also features a large central diamond from Botswana, a country that holds special significance for the couple who have holidayed there together.
Harry has long loved the African country after visiting it many times as a child. The couple will marry in church wedding in the spring next year.
Harry, dressed smartly in a blue suit and dark tie for the open air photocall, revealed of Ms Markle: "When did I know she was the one? Very first time we met."
Ms Markle said she was "so very happy, thank you" to be engaged to Harry.
The prince added that he was "thrilled, over the moon" saying: "Very glad it's not raining as well."
A beaming Ms Markle clutched Harry's hand with both of her hands as they posed briefly, smiling and giggling throughout their appearance in the chill November air.
When Harry was asked how he proposed, Ms Markle replied "Save that", with Harry adding: "That will come later."
The pair waved at the cameras as they walked away arm in arm.
The sunken garden is poignantly the site of the memorial garden created in memory of Harry's late mother Diana, Princess of Wales to mark the 20th anniversary of her death this year.
It was one of the princess's favourite parts of the palace grounds.
Harry and Ms Markle were separated from the media by several metres of water, standing on the other side of the large ornamental pond.
Fifth in line to the throne Harry, 33, has been dating the 36-year-old star, who found fame in the US legal drama Suits, since the summer of 2016 when they met through mutual friends in London.
The Queen and Duke of Edinburgh said they were "delighted" for their grandson and Ms Markle, and "wish them every happiness", while the prince's father the Prince of Wales said he was "thrilled".
The Duke and Duchess of Cambridge reacted warmly to the news.
"We are very excited for Harry and Meghan," they said. "It has been wonderful getting to know Meghan and to see how happy she and Harry are together."
Ms Markle's parents Thomas Markle and Doria Ragland wished their daughter and Harry "a lifetime of happiness", adding: "We are incredibly happy for Meghan and Harry."
The couple are planning to make Harry's current base, Nottingham Cottage at Kensington Palace, their marital home.
Ms Markle will become an HRH and a senior royal after marrying Harry and joining the Windsors.
She is expected to become a duchess, just like Kate Middleton did when she became the Duchess of Cambridge after saying her vows in 2011. But unlike Kate, Ms Markle is not a future queen.
With the arrival of the Cambridges' children, Harry is too far down the line of succession to have a realistic prospect of being monarch.
Ms Markle will most probably become HRH the Duchess of Sussex, if Harry is made the Duke of Sussex by the Queen on the morning of his wedding.
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