Kevin Garnett has committed to returning to the Celtics, agreeing to a three-year contract believed to be worth around $34 million, according to an NBA source. Garnett, an unrestricted free agent, informed the Celtics before Sunday’s start of free agency negotiations, which should help the team accelerate talks with several players.

With Garnett, the Celtics will have five players under contract for the 2012-13 season, including team captain Paul Pierce and Rajon Rondo. Free agent signings don’t become official until July 11; until then, the Celtics will decide whether to bring back unrestricted free agents Ray Allen, Brandon Bass, Jeff Green, and Mickael Pietrus, among others.