Jackson had his contract purchased from Triple-A Gwinnett on Tuesday.
Jackson will take the roster spot of Julio Teheran (thumb), who was placed on the 10-day disabled list in a corresponding roster move. The 26-year-old allowed two runs in a pair of relief appearances (1.1 innings) for the Braves earlier in the season. He'll likely be limited to low-leverage work during his time with the big club.