Also Thursday, the team exercised its option on guard Avery Bradley for the 2012-13 season. Terms of the deals were not disclosed.
Green averaged 9.8 points and 3.3 rebounds with the Celtics last season after coming to Boston in the trade that sent Kendrick Perkins to Oklahoma City.
Bradley averaged 1.7 points in 5.2 minutes per game as a rookie for the Celtics. He was Boston's first-round draft pick, 19th overall.