Green was available for Thursday's game in Boston against the Celtics and entered with about 4:30 left in the first quarter. He contributed a rebound in 11 minutes in the Rockets' 99-98 loss.
The Rockets have until the NBA's deadline of Jan. 7 to guarantee Green's contract for the season or waive him. At that time, Houston could waive Green but still sign him back on a series of 10-day contracts.
The Rockets, with the NBA's second-best record at 25-8, will use Green as insurance for their backcourt depth.
Green's former coach, Celtics coach Brad Stevens, spoke highly of the Rockets' newest acquisition ahead of Thursday's game.
"Gerald's a really accomplished guy. I think it makes a lot of sense [for Houston]. He fits perfect for how they play. I wish they would have waited until tomorrow [to sign him]," Stevens said.
Green, 31, was released at the end of training camp by the Milwaukee Bucks.
Green has had NBA stops with Boston, Minnesota, Houston, Dallas, Brooklyn, Indiana, Phoenix and Miami, as well as stints overseas. He was the No. 18 overall pick in the 2005 NBA draft out of Gulf Shores Academy in Houston. He won the NBA Slam Dunk Contest on All-Star Weekend in 2007.
ESPN's Chris Forsberg contributed to this report.