Bummer, 32, is a reliable reliever who has spent the past eight seasons with the White Sox. He has a career ERA of 3.36 and a WHIP of 1.21.
The Braves hope that Bummer can add depth to their bullpen, which was a weakness of theirs in 2022.
The White Sox are getting a package of young talent in return for Bummer, including Soroka, who is considered to be a top pitching prospect.
Soroka, 25, has been plagued by injuries in recent years, but he has the potential to be a front-line starter.
The other players involved in the trade are right-hander Jared Shuster, infielder Nicky Lopez, infielder Braden Shewmake, and minor league pitcher Riley Gowens.
The trade is expected to be officially announced on Friday.
Bummer is expected to join the Braves' bullpen immediately.
Soroka is expected to be assigned to the White Sox' minor league system.
The trade is a significant one for both the Braves and White Sox, and it could have a major impact on the 2023 season.