Asik met with Rockets officials in Los Angeles as soon as contact with free agents was allowed, and he will count $8.36 million annually against the salary cap. He averaged 3.1 points and 5.3 rebounds in 14.7 minutes per game last season.
Chicago is expected to replace him with a one-year deal with free agent Nazr Mohammed, who played for Oklahoma City last season.
The Bulls' recent flurry of moves made it impossible to match the offer to Asik and stay below the hard salary cap.
Chicago signed Kirk Hinrich, who will start at point guard while Derrick Rose recovers from knee surgery. When Rose returns, Hinrich is expected to come off the bench behind shooting guard Richard Hamilton.
Chicago has been adding guard depth, with Marco Belinelli expected to sign a two-year, $3.8 million deal, according to La Gazzetta dello Sport.