Terry had been contemplating contract offers from the New Orleans Pelicans and Rockets. The lure of playing for a Houston team in the hunt for an NBA title appealed to Terry despite a more lucrative financial package from New Orleans.
A source said Terry would sleep on it before making his decision final on Wednesday. Terry is expected to sign a one-year deal for the veterans minimum.
In 77 games last season, Terry averaged seven points in 21.3 minutes per game. He 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 valued Terry's ability to play both guard positions and his postseason experience -- he's played in 110 career playoff games.
In addition to bringing Terry back, the Rockets are still in talks with second-round pick Montrezl Harrell, with whom the team has yet to finalize a deal.