General manager Chris Wallace announced Green's decision Thursday.
The 6-foot-9, 235-pound Green averaged 16 points, 4.2 rebounds and 1.7 assists in 78 games this season with Boston and Memphis. The Grizzlies acquired him in a three-team trade Jan. 12, and he averaged 13.1 points, 4.2 rebounds and 1.8 assists in 45 games with Memphis. Green shot a team-best 39.8 percent from 3-point range after the All-Star break.
In the playoffs, Green averaged 8.9 points, 4.7 rebounds and 1.7 assists.
Green originally was drafted by Boston fifth overall in 2007. He has started 432 of his 556 games with Seattle/Oklahoma City, Boston and Memphis.