A two-cap Scotland international, Bridcutt has put pen to paper on a three-year contract that promises to keep him at the City Ground until 2020.
The 28-year-old has previously had an impact at Championship level during his time with Brighton. He had helped the Seagulls into the second tier from League One in 2011 and later earned a Premier League switch to Sunderland as a result of his form.
Bridcutt then moved to Leeds on loan in November 2015, a deal that was made permanent at the beginning of last season. He played 25 times in the Championship as Leeds narrowly missed a playoff berth.