Bridcutt made 27 appearances for the Whites last season after initially joining the the club on loan in November under former head coach Steve Evans.
The 27-year-old signed for Sunderland from Brighton for a £3m fee in January 2014, but played in only 30 Premier League games for the Black Cats.
He made his Scotland debut against Serbia in 2013, and won his second cap in a 1-0 win over Denmark in March.