Jansen, 34, has spent his entire 12-year career in the majors with the Dodgers, helping the franchise win a World Series in 2020. He will now pitch for a team in the Braves that bested Los Angeles in the National League Championship Series the following year.
The right-hander had a bounce-back season in 2021, generating his highest average fastball velocity since 2017 and wielding a cutter that recovered some of the mojo he had lost through the years. He finished the season with a 2.22 ERA and 38 saves.
To make room for Jansen on the 40-man roster, Atlanta placed right-hander Jay Jackson on the 60-day injured list because of a right lat strain.
ESPN's Buster Olney contributed to this report.