Terry will sign a one-year deal for the veteran minimum.
Terry also had been contemplating a contract offer from the New Orleans Pelicans, but the lure of playing in Houston for a team in the hunt for an NBA title appealed more to Terry, despite the fact that New Orleans offered more money.
In 77 games last season, Terry averaged seven points in 21.3 minutes per game. Terry moved into the starting lineup late in the regular season and for the entire postseason run when point guard Patrick Beverley suffered a season-ending wrist injury.
The Rockets cited Terry's ability to play both guard positions and his postseason experience (110 career games) as the reasons for his return.
In addition to bringing Terry back, the Rockets are still in talks with second-round pick Montrezl Harrell.