The 20-year-old, who has represented England at under-17 and under-18 level, has put pen to paper on a four-year deal at Vitality Stadium and will join the club's under-23 squad.
Mahoney's contract at Ewood Park expired at the end of June, and the club are continuing to discuss satisfactory compensation with Blackburn.
“I think I'm ready to step up and challenge myself," said Mahoney.
“I'm a young, hungry player, who wants to attack and get past my man.
“I like to get fans off their seat and I'm trying to make my way in the game.
“Working with Eddie Howe and his coaching staff will be a dream come true, so to be able to do that day in, day out will get the best out of me."
“He is a player we have very high hopes for. He has a lot of potential and hopefully it will be a really good deal for both him and us.
“He put in a number of eye-catching appearances for Blackburn in a short space of time at the end of last season, so we quickly evaluated the situation and made a move for him.
“There's a lot more to come from him and we will look to develop his talent."