The person spoke to The Associated Press on the condition of anonymity because Smith hasn't yet cleared waivers.
Smith was let go by the Pistons this week after signing a four-year, $54 million contract in July 2013. The small forward has averaged 15.4 points and 7.8 rebounds during his 11-year career. He averaged 13.1 points and 7.2 rebounds in 28 games this season.
He also is averaging 4.7 assists, 1.3 steals and 1.7 blocks a game this season.
The move will reunite him with AAU teammate and longtime friend Dwight Howard, who is in his second season in Houston. Smith should be a boost to a team that has played the last 23 games without starting power forward Terrence Jones. Jones averaged 14 points and 7.5 rebounds last season, but is out indefinitely with nerve inflammation in his left leg.
The 6-foot-9, 225-pound Smith was the 17th overall pick by the Atlanta Hawks in 2004. He spent his first nine seasons with the Hawks, where he averaged 15.3 points and eight rebounds, before signing with the Pistons.
The Rockets are 20-7 and second in the Southwest Division. Houston's next game is at Memphis on Friday night.