Jon Heyman of MLB Network first reported the deal.
The 34-year-old appeared in 19 games last season for the Milwaukee Brewers and posted a 3.50 ERA, 1.29 WHIP and 78 strikeouts in 87.1 innings. It was a solid bounce-back effort after he finished with a 4.21 ERA during the 2018 campaign while pitching for Milwaukee and the Washington Nationals.
Gonzalez also had an ugly 6.00 ERA in two playoff appearances for the Brewers that season.
While the southpaw has been inconsistent of late, he is not far removed from a strong 2017 when he tallied a 2.96 ERA, 1.18 WHIP and 188 strikeouts in 201 innings. He was also an All-Star in 2011 and 2012 while pitching for the Oakland Athletics and Nationals, respectively.
With eight playoff appearances on his resume, Gonzalez offers a veteran presence to a young White Sox team with plenty of promising pieces as it looks to turn a corner.
Chicago also needed pitching to go with a lineup that features Eloy Jimenez, Jose Abreu and the newly added Yasmani Grandal, among others. While the White Sox weren't able to land the biggest names on the market in Gerrit Cole, Stephen Strasburg and Madison Bumgarner, Gonzalez will help them fill out the rotation.