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.
The Jaguars wanted to keep Tucker all along. He was interim coach after Jack Del Rio was fired in November and interviewed for the head job. Tucker also interviewed to be Minnesota's defensive coordinator.
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.
Mularkey is still interviewing other potential assistants, including several former Jaguars.
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.
The Jaguars are looking to turn Blaine Gabbert into a franchise quarterback. Mularkey still plans to hire a quarterbacks coach.