Veal, 27, takes the roster spot of outfielder Jordan Danks, who was optioned to Charlotte after Sunday's game against the A's.
In 35 appearances with Charlotte, Veal went 7-3 with a 2.08 ERA and 61 strikeouts out of the bullpen. Opponents were hitting .211 against him. From April 26 to June 6, he went 17 1/3 innings without allowing an earned run.
The left-hander was with the White Sox from July 19-22, throwing 1 2/3 scoreless innings, while recording three strikeouts over two relief appearances -- both coming against the Tigers.
"He threw fine, I think that is one of the reasons he is getting the call back up," White Sox manager Robin Ventura said. "He has a good curveball. He was effective against Detroit, not just against lefties, but even against righties. He gave us a different look out of the bullpen, you just aren't bringing in the same kind of guy."
Ventura feels Veal's addition will give relievers Jesse Crain, Brett Myers and Matt Thornton a much-needed breather.
The White Sox are now working with an eight-man bullpen, opposed to the customary seven, and Ventura said there is no timeline for how long he plans to keep that in place.
Chris Toman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.