The 33-year-old ginger-beard prince is the fifth in line to the throne. The 36-year-old Markle is a well-regarded actress who was born and raised in California.
The couple will live at Harry's snug two-bedroom bachelor pad, Nottingham Cottage - known as Not Cot - on the Kensington Palace grounds in London. The announcement said the couple had become engaged earlier this month in London.
More details to come, the palace promised.
The statement was issued by Harry's father, Prince Charles, the Prince of Wales, and Queen Elizabeth II, whom Harry's mother, the late Princess Diana, liked to call "the top lady." It said that Harry was "delighted" and had received the blessing of Markle's parents.
The last time an American married into the royal family, Britain and the monarchy was plunged into crisis. In 1936, King Edward VIII abdicated the throne to marry the American socialite and divorcée Wallis Simpson.
Harry confirmed he was dating the actress in November 2016 when he blasted the tabloid press for subjecting Markle to a "wave of abuse and harassment."
The palace condemned "the smear on the front page of a national newspaper, the racial undertones of comment pieces, and the outright sexism and racism of social media trolls and web article comments."
Markle's mother is African American, and her father is white. She is divorced, without children from the previous marriage.
On Monday, the British media quickly raised the issue of Markle's race, marital status and nationality.
A BBC News alert read: "American, divorced, an actress and mixed race - Meghan Markle will bring something different to the Royal Family."
The Daily Mail's headline informed, "the Queen says she is 'delighted' the divorced American actress is to join the royal family."
The press seemed unsure of the British public's gut reaction to the engagement news, even as most stories asserted that the bride-to-be's race and nationality was either a good thing or irrelevant.
Stephen Bates, former royal correspondent at the Guardian, told the BBC, "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."
Bates added, "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."
But the Guardian newspaper website started one of its live blogs with the tease, "Joy or disdain? Follow the reactions to the royal engagement."
In her career, Markle is best known for playing Rachel Zane in the popular New York City legal drama "Suits," which is filmed in Toronto, where Markle has been living.
London's Evening Standard wondered aloud, what should Ms. Markle be called?
"The most likely situation," the newspaper guessed, "is that Harry and Meghan will actually become known as the Duke and Duchess of Sussex but this depends on the Queen. The Queen must grant the couple a royal dukedom on their wedding day in order for them to be allowed these titles. This is the way that wives of royals can be known on an equal level to their husbands, otherwise Markle will have to get used to being known as Princess Henry of Wales."
The royal family has a long and fraught relationship with the issue of divorce - just ask Queen Elizabeth II's uncle, Edward, who abdicated the throne so he could marry Wallis Simpson, an American divorcée. Markle was previously married to Trevor Engelson, a film producer. They wed in 2011 and split after two years.
When Harry's father Charles married Camilla - they were both divorcées - the couple opted for civil ceremony.
But divorce isn't the big deal it once was - three of the queen's four children are divorcées - and there's no reason to think that Harry and Meghan couldn't be married in a Church of England ceremony, especially after they clarified their position on the subject of divorce.
In 2002, the Church of England's governing body said that "there are exceptional circumstances in which a divorced person may be married in church during the lifetime of a former spouse." Whether or not to perform the marriage in a church is a decision that "rests with the minister," they said.
If that minister was Justin Welby, the Archbishop of Canterbury - the most senior post in the Church of England - it seems likely that he would happily oblige.
"I'm absolutely delighted to hear the news that Prince Harry and Meghan Markle are now engaged," he tweeted. "I wish them many years of love, happiness and fulfillment - and ask that God blesses them throughout their married life together."
Within seconds of the royal engagement being announced, Twitter erupted in celebration. "Harry and Meghan" and #Royalengagement quickly began trending in the UK and worldwide as people offered their congratulations.
"They look so in love and make such a lovely couple. This is great for Britain as a whole. Next year is going to be all about #harryandmeghan," tweeted one user.
Kensington Palace said, "Ms. Markle's parents, Mr. Thomas Markle and Doria Ragland, have wished the couple 'a lifetime of happiness.'"
Britian's prime minister, Theresa May, perhaps relieved to put the drudgery of Britain's exit from European Union aside for an hour, added her voice, "I would like to offer my very warmest congratulations to HRH Prince Harry and Meghan Markle upon their engagement. This is a time of huge celebration for two people in love. On behalf of myself, the government and the country, I wish them great happiness for the future."
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)