Terms of the deal haven't been announced.
Green, 27, is coming off the most productive season of his career. A 6-foot-9 forward, he averaged 8.9 points, 7.1 rebounds, 1.1 assists and 27.3 minutes last season in 77 games for the Grizzlies, including 75 starts.
Green has played 179 games in a three-year NBA career with the Grizzlies and San Antonio Spurs and has career averages of 7.4 points and 5.4 rebounds.
Green went undrafted after a four-year career at Alabama. He played professionally in the NBA G League and in France before making his NBA debut with San Antonio in January 2015.