Asik signed the Rockets' offer sheet Friday in Chicago after meeting with Rockets Coach Kevin McHale in Las Vegas, the Chicago Tribune reported.
The 7-foot, second-year front-courtman averaged 3.1 points and 5.3 rebounds per game in 66 games for the Bulls last season.
Asik helped lead Turkey to a silver-medal-winning performance at the 2010 FIBA World Championships.
"We are excited to add Omer to our roster," Rockets General Manager Daryl Morey said. "Omer has proven to be a defensive force at every stop in his career -- in the Turkish league, in FIBA's World Championships and EuroBasket competitions, and of course for the past two years for the Chicago Bulls."
"We have decided not to match Houston's offer sheet for restricted free agent Omer Asik," Bulls GM Gar Forman said. "It was a difficult decision because Omer did a nice job for us."
The Rockets also announced Tuesday they had waived guard E'Twaun Moore.