ESPN's Adrian Wojnarowski initially reported Green and the Rockets were in the process of finalizing a non-guaranteed contract.
Green signed with the Milwaukee Bucks in September before being released on Oct. 14, four days before they opened the regular season.
The 31-year-old journeyman has played for eight teams in his 10-year NBA career, including the Rockets, Boston Celtics, Phoenix Suns, Miami Heat, Indiana Pacers, Dallas Mavericks, New Jersey Nets and Minnesota Timberwolves. He also played in professional leagues in Russia and China from 2010-2012.
Green's last appearance in an NBA game was with the Celtics in Game 5 of the 2017 Eastern Conference Finals against the Cavaliers. He played in one game for the Rockets during the 2007-08 season.
The Rockets need depth to fill out their bench with Chris Paul, Luc Mbah a Moute and Clint Capela dealing with injuries.