Pittsburgh received right-handed pitcher Yordi Rosario and international slot money from Chicago.
Nova, 31, went 9-9 with a 4.19 ERA in 29 starts with Pittsburgh last season. He is 78-64 with a 4.26 ERA over parts of nine combined seasons with the Pirates and New York Yankees.
"It doesn't necessarily preclude us from doing anything else with the rotation, but it was important for us to find some sort of veteran presence as we entered later in the offseason," White Sox general manager Rick Hahn said of acquiring Nova.
"As we entered this offseason he was on the list of guys that could fit this role," Hahn added. "This was an important get as far as stabilizing the rotation."
Chicago will be without promising young starter Michael Kopech for all of 2019 after the right-hander underwent Tommy John surgery in September.
"We think (Nova's) going to be able to eat up some innings and pitch effectively for us,'' Chicago manager Rick Renteria said. "I think the front office was doing their due diligence in trying to acquire someone of Nova's status and stature, and all the reports from everybody we've spoken to, this kid's a good pick up for us.''
Rosario, 19, had a 2.57 ERA and 70 strikeouts in 14 appearances (11 starts) in 2018 between the Dominican summer league and Arizona Fall League.
In addition to Rosario, the Pirates in a separate move added veteran right-hander Jordan Lyles, according to multiple reports.
News of the Lyles free-agent transaction was first reported by the New York Post.
He is 31-52 with 2 saves and a 5.28 ERA in eight major league seasons.
Information from The Associated Press was used in this report.