As part of the deal, the Warriors dealt guard Toney Douglas to the Miami Heat, who in turn sent center Joel Anthony to the Celtics, along with a protected future first-round pick, a 2016 second-round pick and cash.
The key to the deal is Crawford, a point guard who was averaging 13.7 points and 5.7 assists per game for Boston. He nabbed Eastern Conference Player of the Week honors last month, but his production has tailed off since then.
Brooks is averaging 3.1 points per game. His and Crawford's departure will free up roster spots for Boston, including one for Rajon Rondo, who is expected to return to the Celtics' lineup Friday.
By unloading Anthony, the Heat will save $11.5 million in salary and luxury tax.