The 31-year-old Jackson was released by the Cubs on July 27 after designating him for assignment the week before.
The team had signed Jackson to a four-year, $52 million deal in 2012 to be an anchor of their rotation, but after that didn't work out, he became a long reliever.
Jackson's poor performances as a starter made the deal a failure and the Cubs felt that they would be better off without him, despite his success out of the bullpen and the fact that they owed him $11 million for 2016.
The Braves signed Jackson just through this season, so it's unlikely that he will become anything more of an innings eater for them. However, it's possible that they could put him through trade waivers and deal him, as they don't owe him a penny of the Cubs contract, and he could help a contender down the stretch out of the bullpen. If they were to make a move, it would have to come before August 31, the waiver trade deadline.
On the season, Jackson is 2-1 with a 3.19 ERA (2.88 FIP) in 31 innings, posting a 23 to 12 strikeout-to-walk ratio. His 120 ERA+ is the highest it has been since 2011 with the Cardinals.