The 20-year-old Wales international, who has agreed a four-year contract, scored three goals in 30 league appearances for the Championship side.
The Bournemouth Echo reported the Cherries will pay a fee of £10m, potentially rising to £11.5m.
"We've seen enough to suggest he could be outstanding at this level," said Bournemouth boss Eddie Howe.
"He is technically very good, has huge potential and will fit our philosophy in terms of how we want to play."
Brooks represented England at under-20 level but 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.
Source: BBC NEWS