Belisario, 31, was 4-8 with a 5.56 ERA and eight saves in 62 relief appearances in his lone season in Chicago. He signed as a free agent in December.
The White Sox also purchased the contracts of pitcher Frankie Montas, infielders Rangel Ravelo and Tyler Saladino and catcher Kevan Smith. They outrighted outfielder Jared Mitchell to Triple-A Charlotte and claimed left-hander Onelki Garcia off waivers from the Los Angeles Dodgers.
Thursday's moves put Chicago's 40-man roster at 40.