The 18-year-old Scot has signed a three-and-a-half-year deal at the Goldsands Stadium.
Having come through the Dons' youth ranks, Fraser made his debut in 2010 but only became a first-team regular in the last few months.
"He is a talented lad," Cherries boss Eddie Howe told the club's official website. "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."
Fraser has made 18 appearances so far this season and made his Scotland Under-19 bow against Germany back in August.