Atlanta optioned Brebbia to Triple-A Gwinnett on Saturday.
Atlanta signed Brebbia to a one-year contract and added him to the active roster Sunday.
The White Sox released Brebbia on Thursday, Scott Merkin of MLB.com reports.
The White Sox designated Brebbia for assignment Tuesday, James Fegan of SoxMachine.com reports.
Brebbia (0-6) allowed three earned runs on one hit and one walk while recording one out to take the loss Monday against the Royals.
The White Sox activated Brebbia (calf) from the 15-day injured list Monday.
Brebbia (calf) will begin a rehab assignment with Triple-A Charlotte on Friday, LaMond Pope of the Chicago Tribune reports.
Brebbia was placed on the 15-day injured list Monday with a left calf strain, retroactive to April 6.
Brebbia pitched a perfect ninth inning in Saturday's 7-6 extra-inning loss to the Tigers.
Brebbia (calf) went through fielding drills Wednesday, Daryl Van Schouwen of the Chicago Sun-Times reports.