Green, a native of Houston, signed a 10-day contract with the Rockets on Dec. 28 and ended up staying for the season. He averaged 12.1 points and 22.7 minutes during his 41 games with the Rockets.
"For all the hard work I've been putting in and all my dreams, it felt good," Green told the Houston Chronicle. "Everybody knows in my heart where I wanted to be. It's tough to leave my home."
Green, 32, has averaged 9.8 points and 19.7 minutes in 585 regular-season games. The 11-year NBA journeyman has also played for the Celtics, Timberwolves, Mavericks, Nets, Pacers, Suns and Heat.