Jackson coached in Cincinnati from 2012 to 2015 in a variety of roles, ending with a two-year stint as offensive coordinator that earned him the top job in Cleveland.
The Browns fired the 53-year-old at the end of October after he amassed a record of 3-36-1 during his tenure with the team. Jackson will get a chance at revenge, though, as the Bengals play the Browns in Weeks 12 and 16.
It's the second significant coaching move of the day for the Bengals, who fired defensive coordinator Teryl Austin after allowing 51 points to the New Orleans Saints in Week 10. Head coach Marvin Lewis is set to take over the defense.