Agent Mitchell Butler confirms the deal Wednesday for Bradley, the No. 19 pick in the 2010 draft.
Bradley averaged a career-best 14.9 points in 60 games last season as the starting point guard while Rajon Rondo was recovering from a torn knee ligament. Bradley can play either guard spot and is a strong defender.
The Celtics extended a qualifying offer to Bradley on Monday, making him a restricted free agent and allowing them to match any offer he received from another team.