Meghan, then best known for her role in legal drama Suits, immediately said the feelings were reciprocal and the pair started talking about their future together.
In Finding Freedom, serialised by the Times and the Sunday Times, co-authors Omid Scobie and Carolyn Durand wrote the couple went on dates in London, Toronto and Botswana as the relationship bloomed.
Three months into their relationship, a Meghan friend said, they had already begun swapping the words 'I love you'
The book, due to be released on August 11, said: “For Meghan, she was all in. Nothing could get her to slow down, not even a friend who cautioned her about getting involved with Harry.
“Three months into their relationship, a Meghan friend said, they had already begun swapping the words ‘I love you’.
“It was Harry who said it first, but Meghan immediately replied, ‘I love you, too.’
“From there it didn’t take long for them to begin talking in non-oblique terms about their future.”
The book also detailed how the now Duchess of Sussex left “clues” about the romance before it became public, including posting a photo of a Love Hearts candy with the inscription Kiss Me and the caption “Lovehearts in #London” to Instagram on the night of a date.
She also began to follow an Instagram account with the username @Spikeymau5 which, the co-authors said, was Harry’s private account.
Spike apparently came from a Facebook alias that he used – Spike Wells – while the second half of the moniker was a nod to one of his favourite DJs Deadmau5.
A spokesman for the Sussexes told the Times: “The Duke and Duchess of Sussex were not interviewed and did not contribute to Finding Freedom.”