Baxter Holmes of the Boston Globe reports that he can confirm a deal has been reached and that it's worth $32 million over four years.
The Celtics had made a qualifying offer worth $3.6 million to Bradley on Monday, allowing them to match any outside offer that he received once free agency began. The Philadelphia 76ers were also reportedly interested in the 23-year-old, but Bradley had expressed his desire to remain in Boston.
A former 2010 first-round draft pick, Bradley had his best NBA season to date in 2013-14, averaging 14.9 points per game while shooting 43.8 percent from the floor and 39.5 percent from three.
"I think Avery can be a very key player in us winning the championship. He does things that other players can't do. His shooting continues to improve, we all have all seen his terrific defensive abilities. I think Avery is a big part of [the team's future]," Celtics president of basketball operations Danny Ainge said on Monday.