Green finished last season with the Rockets after signing with them in February. He started the 2019-20 season with the Utah Jazz but was waived in late December.
The 34-year-old averaged 9.4 points and 2.8 rebounds in 20 minutes per game last season.
Green has a history with Nets star Kevin Durant. The two were rookies together with the Seattle SuperSonics in 2007 and remained teammates until the Oklahoma City Thunder traded Green to the Boston Celtics during the 2010-11 season.