Bradley, 22, has been out roughly seven months after undergoing surgery on both shoulders.
"My teammates are excited, I'm excited," Bradley told reporters Tuesday. "I'm pretty sure the fans are excited. We're just going to go out there and play Celtic basketball tomorrow."
The Celtics have started the season a disappointing 14-16, losing seven of their last 10.
Bradley is a defensive impact player the Celtics hope can restore some of their dominance on that end of the floor. Boston has really slipped lately defensively, falling to 14th in defensive efficiency, giving up 102.1 points per 100 possessions.
He's also a lethal corner 3-point shooter who will help space the floor. Last season Bradley shot 40.7 percent from three.