The White Sox made the move Friday.
Drabek spent most of 2014 at Triple-A Buffalo. He made two appearances with Toronto, working three scoreless innings.
Over parts of five seasons with the Blue Jays, the 27-year-old righty went 8-15 with a 5.27 ERA.
The White Sox put right-hander Nate Jones on the 60-day disabled list. He was limited to two games last year because of hip and elbow injuries.