In return for Kimbrel, the White Sox sent second baseman Nick Madrigal and right-handed relief pitcher Codi Heuer to the Cubs in the trade. Madrigal, a rising star in the league, is out for the season due to a torn right hamstring.
The White Sox already had one of MLB's top closers in All-Star right-hander Liam Hendriks. The club now adds Kimbrel, who has a 0.49 ERA and 23 saves in 25 opportunities for the Cubs this season.
Kimbrel also leads National League relievers in strikeout rate and opponents' batting average. He ranks ninth in league history with 371 career saves during his 12 years in the majors.
White Sox manager Tony La Russa said he has a plan for how to use both Hendriks and Kimbrel, but he declined to provide specifics.
"On any given day, one may be available, the other one may not be," White Sox general manager Rick Hahn told reporters Friday. "It puts us in a position where we have a very dynamic and impactful bullpen regardless of the situation that arises in each game."
The 24-year-old Madrigal, who was the No. 4 overall pick in the 2018 amateur draft, had a .305 batting average with a .354 on-base percentage over 54 games this season before his injury.
Heuer, 25, has a 4-1 record and 5.12 ERA in 40 appearances this year.
The White Sox entered Friday with an eight-game lead over the Cleveland Indians in the American League Central. The Cubs are fourth in the NL Central and appear to be in rebuild mode.