However, in a TV interview with the BBC, the couple say Harry popped the question over a typical night for the pair that included a low-key roast dinner, in November 2017.
Speaking about the moment, Meghan said: "Just a cosy night, it was - what we were doing just roasting chicken and having …"
Interrupting his fiancee, Harry said: "Roasting a chicken, trying to roast a chicken."
Meghan continued: "Trying to roast a chicken and it just - just an amazing surprise, it was so sweet and natural and very romantic. He got on one knee."
Harry added: "She didn't even let me finish, she said can I say yes, can I say yes and then were was hugs and I had the ring in my finger and I was like can I - can I give you the ring? She goes - oh yes the ring.
"So no it was - it was a really nice moment, it was just the two of us and I think managed to catch - catch her by surprise as well."
The book is set to be released August 11.
The bombshell biography also says Kate Middleton "purposely" snubbed Meghan and "barely acknowledged her" as the royal wives made their final appearance together.
The book's authors, Omid Scobie and Carolyn Durand, said: "Although Meghan tried to make eye contact with Kate, the duchess barely acknowledged her."
Scobie told the Times: "To purposefully snub your sister-in-law... I don't think it left a great taste in the couple's mouths."
Finding Freedom, serialised by the Times and the Sunday Times, contains sensational new claims about how Meghan and Harry's relations with his family broke down, and how the Sussexes decided to quit life as senior royals.
A spokesman for Harry and Meghan said the couple did not contribute to the book.
However, the spokesman did not deny any content of the extracts made public so far.