New coach Mike Mularkey also kept defensive line coach Joe Cullen and linebackers coach Mark Duffner.
Mularkey announced the hires Friday, his first personnel decisions since taking over Tuesday. Mularkey also gave Tucker the title of assistant head coach.
Jacksonville's defense flourished under Tucker last season, finishing sixth in the league despite several key injuries. Cullen and Duffner were key parts of the unit.
Bratkowski spent last year working with Mularkey in Atlanta. Before that, he spent 10 seasons as Cincinnati's offensive coordinator and got credit for helping mentor quarterback Carson Palmer.