The 18-year-old has signed a three-and-a-half year contract with the npower League One club after rejecting a new deal at Pittodrie.
Fraser, who won two Clydesdale Bank Premier League young player of the month awards this season but has not yet played 90 minutes, was out of contract at the end of the season.
Dons chief executive Duncan Fraser said on the club`s website: "Right from the start we indicated that we had no desire to see Ryan move and that if it were to happen, a bid well above the training compensation fee due in the summer and with add ons would need to be forthcoming.
"Following detailed negotiations AFC Bournemouth came back with an offer that was acceptable to the club, and given the fact that they were free to talk to Ryan and could have signed him on a pre-contract, it was only right that we allowed Ryan to speak to Bournemouth with as little coverage as possible, which was what all parties agreed.
"This allowed Ryan to make up his own mind about what he wished to do and, although disappointed he is moving on, I and the club need to respect what he has decided and we all wish him the very best for the future.
"It is worth pointing out that eight young players have signed contract extensions over the last few weeks and we remain absolutely committed to youth development as the way ahead for this club, understanding that along the way some players will choose to move on at the end of their contracts."
Bournemouth manager Eddie Howe told his club`s 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."