The highly-rated 18-year-old was being chased by a number of clubs but opted to move to the Goldsands Stadium, where he has signed a three-and-a-half year deal.
Fraser made 18 appearances for the Dons this season and he was named SPL Young Player of the Month in September and October.
Boss Eddie Howe told Bournemouth's official website: "He is a talented lad.
"He's only 18 but he's very, very highly regarded in the world of football, especially up north and Aberdeen were desperate not to lose him.
"He came to our attention a while back and he's someone that we have tracked for a long period of time. We had a lot of competition for his signature but the fact we were able to sign him is a real positive for his football club.
"There will be a period of adjustment for a young lad to come all this way but we will look after him and do all the work we need to do with him to try and improve his game. If we can and the move goes as well as we hope it can, I think we have got a top player on our hands."