The 20-year-old Wales international has signed a four-year deal for an undisclosed fee.
He told the Cherries' website: "The chance to come and play for a club in the Premier League is a great opportunity for myself. I'm delighted to be on board.
"When you look at Eddie Howe as a manager you want to be involved in something like that. He's got big ambitions and with younger players he develops them well and he gives them a chance.
"That's something I'm looking for and he was one of the main attractions for me to come to Bournemouth."
Brooks represented England at under-20 level but switched allegiances to Wales and has been capped three times.
Bournemouth boss Howe said: "David is a player we have been looking at for a long time.
"He is technically very good, has huge potential and will fit our philosophy in terms of how we want to play.
"We've seen enough to suggest he is a player who could be outstanding at this level in the future if he develops in the right way and is willing to learn and improve."
Sheffield United released a statement which confirmed they had received a "club-record fee" for the youngster, and added: "United moved last season to reward Brooks with a new long-term deal and had no intentions to sell.
"However, following changes to his representation, interest from the Premier League proved a key driver in the player wanting to make the move, with the Blades forced to negotiate the best possible transfer fee, plus additional clauses, including a sell-on percentage."
