The 18-year-old, who had attracted interest from a number of Premier League clubs, has penned a three-and-a-half-year deal with the Cherries.
Manager Eddie Howe told the Daily Echo: "He is someone we have brought in very much for the future. He is not necessarily going to be involved straight away, which he is aware of.
"But with a lot of hard work and a good attitude, we could have a really good player on our hands in the not too distant future.
"We are excited by him and are looking forward to working with him but don't want to put too much pressure on him too soon. It is a big jump so we are going to need a bit of patience from everybody."