Vazquez is flying to Atlanta on Wednesday morning for a physical.
A baseball source told ESPN's Peter Gammons that the deal will include four other players, including reliever Boone Logan, who would also go from the White Sox to the Braves.
Among the players expected to go from Atlanta to the Chicago organization are pitcher Jo-Jo Reyes and infielder Brett Lillibridge.
Other Braves players reportedly under discussion to be sent to the White Sox are catcher Tyler Flowers, third baseman Jon Gilmore, and pitcher Santos Rodriguez.
With obvious holes in the rotation, Braves general manager Frank Wren has said he hopes to add two starting pitchers this winter. Atlanta pursued Padres ace Jake Peavy before Wren said last month "we have moved on and shifted our focus" after San Diego didn't agree to what he called "a strong package of players."
Braves right-hander Tim Hudson had elbow ligament replacement surgery on Aug. 7. Aging veterans John Smoltz and Tom Glavine also had season-ending arm operations, and their status for 2009 remains uncertain. Both are free agents.
Left-hander Mike Hampton reached a tentative agreement to sign with Houston.
Vazquez, 32, was 12-16 last season for the White Sox with a 4.67 ERA in 33 starts. He struck out 200 batters in 208 1/3 innings. But his future with the White Sox appeared dim after manager Ozzie Guillen said in September that he wasn't a big-game pitcher. In his last three regular-season starts and the playoff opener against Tampa Bay, Vazquez was 0-4 with a 13.22 ERA.
Logan, a left-handed reliever, was 4-4 with a 5.70 ERA out of the White Sox's bullpen last year. He had a 2-3 record in 55 appearances.
Reyes was 3-11 with a 5.81 ERA last season for the Braves. He started 22 games.
Lillibridge appeared in 90 games at Triple-A Richmond in the Braves' organization. He hit .220 with four home runs and 39 RBIs.
Information from The Associated Press was used in this report.