The 26-year-old only signed a permanent deal in February following a three-month loan deal from Bolton but he made only five league starts in his second spell with the club.
Bridges began his career in Wearside, scoring 21 goals in 92 appearances before making a £5m move to Leeds in July 1999.
The North Shields-born player enjoyed a successful first season at Elland Road, scoring 21 goals, but endured a terrible run of injuries and after a loan spell at Newcastle he joined Bolton on a free transfer.
He returned to the Stadium of Light in September 2004 and ended a four-and-a-half-year spell without a goal by scoring the winner against Stoke in November.