The 33-year-old British royal said in a joint interview with Markle for the BBC that he popped the question while cooking a roast chicken dinner with the 36-year-old American actress.
"It happened a few weeks ago," Prince Harry said. "Earlier this month, here at our cottage. Just a standard, typical night for us ... roasting a chicken."
"It was just an amazing surprise," Markle added. "It was so sweet and natural and very romantic. He got on one knee. As a matter of fact, I could barely let [Prince Harry] finish proposing. I was like, 'Can I say yes now?'"
Prince Harry's father, Prince Charles, had confirmed the couple's engagement in a post on the Clarence House official Twitter account Monday.
"His Royal Highness The Prince of Wales is delighted to announce the engagement of Prince Harry to Ms. Meghan Markle," the tweet read.
"The wedding will take place in spring 2018. Further details about the wedding day will be announced in due course. His Royal Highness and Ms. Markle became engaged in London earlier this month. Prince Harry has informed Her Majesty The Queen and other close members of his family. Prince Harry has also sought and received the blessing of Ms. Markle's parents. The couple will live in Nottingham Cottage at Kensington Palace."
The Prince of Wales is delighted to announce the engagement of Prince Harry to Ms. Meghan Markle. pic.twitter.com/zdaHR4mcY6— Clarence House (@ClarenceHouse) November 27, 2017
"We are incredibly happy for Meghan and Harry. Our daughter has always been a kind and loving person. To see her union with Harry, who shares the same qualities, is a source of great joy for us as parents," said Markle's parents, Thomas Markle and Doria Ragland. "We wish them a lifetime of happiness and are very excited for their future together."
Ms. Markle's parents, Mr. Thomas Markle and Doria Ragland have wished the couple 'a lifetime of happiness.' pic.twitter.com/H4kpTgpkYE— Kensington Palace (@KensingtonRoyal) November 27, 2017
"We are very excited for Harry and Meghan. It has been wonderful getting to know Meghan and to see how happy she and Harry are together," said Prince William and Kate Middleton.
"The Queen and The Duke of Edinburgh are delighted for the couple and wish them every happiness," said The Royal Family Twitter account.
Prince Harry and Markle, who plays Rachel Zane on Suits, were first linked in October 2016. The pair made their first official appearance as a couple at the Invictus Games in Toronto, Canada, in September.