Omogrosso, 29, joined the Sox before Wednesday night's game against the Texas Rangers. He learned of his promotion at 1 a.m. and was in the visitors clubhouse in Arlington 12 hours later.
In 17 relief outings with the White Sox as a rookie in 2012, Omogrosso had a 2.57 ERA with 18 strikeouts in 17 innings. He allowed only one earned run in his final seven appearances, a span of nine innings.
With Charlotte this season, Omogrosso is 0-1 with a 6.52 ERA with nine strikeouts in seven 9.2 innings.
"I was nervous last year with it being my first time up," the 6-foot-4, 240-pounder said. "It helps to have another year of experience and knowing the guys more. You play your whole life for this opportunity."
White Sox manager Robin Ventura said Veal had "things he needed to work on," but the team doesn’t have the luxury to wait for development.
Veal, 28, was 1-0 with a 4.26 ERA in 6 1/3 innings and one hold in 12 relief appearances.
Veal was brought in to face left-handed hitting Mitch Moreland but was touched for an RBI double, the first of six Texas runs in the sixth inning of a 10-6 White Sox loss Tuesday.
Ventura said that after this move, the White Sox will be less likely to call on a reliever to work just one batter with fewer left-handers in the bullpen.