The White Sox selected Burke's contract from Triple-A Charlotte on Tuesday.
The right-hander is up with Chicago for his first taste of the big leagues after posting a 4.62 ERA, 1.29 WHIP and 86:36 K:BB over 64.1 frames in Charlotte's rotation. Burke should immediately be available out of the bullpen for the White Sox, but it's possible he's given a start or two with Nick Nastrini being sent to Triple-A in a corresponding transaction.