NFL.com's Steve Wyche reported the team has added "assistant head coach" to Tucker's title, according to a source with knowledge of the situation. Tucker was elevated to interim head coach for the final five weeks of the season after Jack Del Rio was fired.
New coach Mike Mularkey made the hires late Thursday, his first personnel decisions since taking over Tuesday.
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 Associated Press contributed to this report.