The highly-rated 20-year-old midfielder has completed his move to the Vitality Stadium for an undisclosed fee, having impressed as he progressed through the ranks at Bramall Lane.
The talented youngster has made 37 appearances in all competitions for Sheffield United, netting three times, since his debut in August 2016.
“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,” Brooks told Bournemouth’s official site.
Brooks said the manager was a key factor in his decision to join the south coast side.
“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.”
The Warrington-born youngster progressed through the Sheffield United academy, having moved there in 2014, after being on the books of Manchester City since he was seven.
Manager Howe praised his new signing: “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.
“I believe he has a very exciting future and I’m delighted that future will be here at Bournemouth.”
Brooks represented England at U-20 level, but recently switched allegiances to Wales – the country of his mother’s birth – and won the first of his three senior caps in a friendly fixture against France last November.