The 29-year-old cleared waivers on Wednesday (Dec. 24), just two days after Detroit let him go halfway into his four-year, $54 million contract.
The Rockets are currently three games behind the league-leading Golden State in the Western Conference standings and just a half-game behind Memphis for the 3 seed.
ESPN says Houston assured Smith that he would start if he joined the team, which helped make up his mind over the Mavs, Heat, Kings, Clippers and Grizzles — who were all listed as potential destinations for him.
The Rockets also had their biannual exception, valued at $2.1 million, to offer Smith.
Houston will play the Grizzlies on Friday (Dec. 26).