Prince Harry, aged 33, and Ms Markle, aged 36, are to marry in the spring
He said the "stars were aligned" when they fell in love and he proposed over roast chicken
Appearing for photos outside Kensington Palace earlier, Prince Harry said he was "thrilled"
The couple secretly got engaged earlier this month
The Queen and Prince Philip are "delighted for the couple"
Ms Markle is an actress and humanitarian campaigner
Democratic Unionist Party (DUP) leader Arlene Foster congratulated the wrong prince on his engagement.
As our colleagues report: "Mrs Foster mistakenly tweeted her best wishes to Harry's already-married brother Prince William."
Image source, TwitterShe quickly deleted the tweet and corrected the error.
Image source, PANot excited about the royal engagement?
Jane Hill has been reporting live from Kensington Palace, where the couple will live - and asking people how they feel.
"A lot of the British people I've been talking to are fairly nonplussed, I’ve got to say. They say: well, that’s nice, young couple in love, that’s lovely.
"That’s about as much enthusiasm as I’ve been able to summon up.
"We’ve been talking to a few Americans, who were very, very excited that Prince Harry was going to be marrying an American – now that’s not to say, from those who I’ve managed to speak to in the last couple of hours, that they knew who Meghan Markle was.”
Robert Hardman, a Daily Mail journalist who has written a book on the Queen, says it is no longer an issue for the royal family that Meghan Markle has been married before.
Ms Markle married film producer Trevor Engelson in 2011 before divorcing two years later.
He told the BBC: "No I don't think so at all. I mean in years gone by yes of course that would have been a major issue, that goes without saying.
"But I mean life has changed. You know the Prince of Wales married the Duchess of Cornwall in 2005, and we live in different times."
The head of the Catholic Church in England and Wales has offered his congratulations:
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Image source, ReutersStephen Bates, former Royal correspondent at the Guardian, told the BBC earlier that Ms Markle's mixed-race heritage is not an issue for the British public.
"It’s not entirely unknown that royals have married people of mixed race before. I think people in this country, certainly, are very comfortable with that these days," he said.
"Fifty years ago... it would have been an issue then, but today I would have thought people would take it as not only absolutely commonplace, but rather welcome that the royal family has moved into that generation as well."
Need a refresher?
Prince Harry and Meghan Markle from the beginning
The writing may have been on the wall for the royal engagement when, two weeks ago, the British tabloids reported that Ms Markle was planning on bringing her two dogs to the UK.
Her Instagram account has been silent for months, but hosts plenty of older photos of her four-legged friends Guy and Bogart:
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By BBC royal correspondent Daniela Relph
Image source, Getty ImagesThis is no ordinary royal engagement.
Meghan Markle brings something different to the British Royal Family.
She is American, divorced, an actress and mixed race.
She is also a campaigner with a variety of humanitarian interests and won't want her marriage to limit her ability to speak out and support various causes - particularly those of gender equality.
Image source, Getty ImagesLabour leader Jeremy Corbyn has wished Prince Harry and Meghan Markle "well" following the annoucement of their engagement.
During a speech in Glasgow, he said: “I wish them well, hope they have a great time and great fun together.
“Having met Harry a couple of times I’m sure they’re going to have a great deal of fun together."
Image source, AFPWhen the prince officially confirmed he was dating Meghan Markle in November 2016, he also took the opportunity to condemn Ms Markle's treatment by the press.
He referred to a "smear" on the front page of a national newspaper, racial undertones in comment pieces and "outright sexism and racism" from online trolls.
There had been a "bombardment of nearly every friend, co-worker, and loved one in her life", the prince said.
He was worried about her safety and was "deeply disappointed" to not have been able to protect her.
The Daily Mirror's Royal Correspondent, Victoria Murphy, said it showed Harry's "strong desire to both protect her and hang onto her".
There has been some speculation about the possible venue for a royal wedding - particularly since Ms Markle is a divorcee.
The decision on whether a divorced person can marry in a Church of England church is at the discretion of the individual priest or bishop.
But the Archbishop of Canterbury - the leader of the worldwide Anglican communion - may have hinted at his position in tweeting congratulations to the couple.
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Stephen Bates, former Royal correspondent at the Guardian and author covering the royal family, told BBC News the royal family would favour a traditional church wedding.
"I guess that would be a fairly high priority. Certainly the Queen and the Duke of Edinburgh would like that, and I guess Charles and Camilla too," he said.
"So I would think there will be a royal wedding, it will be in a church, and it will be in Britain."
Image source, ReutersThe couple met through mutual friends in London in July 2016 when one of Meghan Markle's close friends, Markus Anderson, reportedly introduced her to the prince.
Mr Anderson, who sat next to Ms Markle at the Invictus Games opening ceremony in September, is linked with private members club Soho House - of which Harry is a member.
But it wasn't until months after the initial London meeting that the press managed to get news of their blossoming romance.
The Sunday Express was the first paper to reveal the 36-year-old was Prince Harry's new girlfriend with the news featuring on the front page last October.
In the days after it broke, the pair went to a Halloween party where the prince reportedly donned a mask and went trick-or-treating.
Image source, Getty ImagesMs Markle, who plays Rachel Zane in US TV drama "Suits", was born on 4 August 1981 and grew up in Los Angeles but now lives in Toronto.
Her father was a cinematographer on the hit 80s show "Married...with Children" and her first television appearance in the US was in an episode of the medical drama "General Hospital" in 2002, before moving on to roles in "CSI, Without A Trace" and "Castle".
Ms Markle then began appearing in major Hollywood films, including "Get Him To The Greek", "Remember Me" and "Horrible Bosses".
She has also appeared in the sci-fi series "Fringe", playing FBI special agent Amy Jessup,
In September 2011, she married film producer Trevor Engelson after dating for seven years, but the pair divorced two years later.
Kensington Palace tweets...
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The instant Prince Harry and Ms Markle are pronounced "man and wife" she will automatically become Her Royal Highness, Princess Henry of Wales.
However, she does not automatically become Princess Meghan - because she is not of royal blood.
The Queen's late sister Margaret was entitled to call herself Princess Margaret. The Queen's daughter is Princess Anne and her granddaughters are Princess Beatrice and Princess Eugenie.
Royal Family tree and line of succession
The Queen's great granddaughter, Prince William's daughter, is Princess Charlotte. All of these are, or were, of royal blood and so are princesses in their own right.
But Princess Charlotte's mother, the Duchess of Cambridge, is not known as Princess Catherine. Just as Sarah Ferguson was never Princess Sarah and Sophie Rhys-Jones (wife of Prince Edward) is not Princess Sophie.
Lady Diana Spencer was never officially Princess Diana. She was the Princess of Wales and, after her divorce from Prince Charles, she was Diana, Princess of Wales.
Image source, Getty Images
Image source, Getty ImagesSpeaking for the first time about her love for Prince Harry, Ms Markle told Vanity Fair magazine in September: "We're two people who are really happy and in love".
She said the pair were enjoying a "special" time together, adding: "I'm sure there will be a time when we will have to come forward and present ourselves and have stories to tell, but I hope what people will understand is that this is our time.
"This is for us. It's part of what makes it so special, that it's just ours. But we're happy. Personally, I love a great love story".
Kensington Palace tweets...
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