The Braves announced the deal Monday, bolstering a bullpen that didn't have anyone with double-figure saves last season.
Johnson saved nine games for the Braves before he was dealt to the Dodgers at the trade deadline. After posting a 2.25 ERA in 49 games with Atlanta, the right-hander was 0-3 with a 10.13 ERA in 23 games with the Dodgers.
Johnson could have a shot at being the Braves' closer or serving as a setup reliever for Arodys Vizcaino, who had nine saves and a 1.60 ERA in 36 games after taking over the role.
Johnson's deal includes performance bonuses. He earned $1.85 million this year, including $250,000 in bonuses based on games.