The Scotland international will remain at St Andrew's until June 30, 2014 after boss Lee Clark activated a clause in the 29-year-old's contract to ensure a further year's stay.
After joining Blues from Cardiff in July 2011, Burke has found the net 22 times in over 100 appearances and, in his debut season, helped the club to the npower Championship play-offs where they lost to Blackpool in the semi-finals.
Meanwhile, club captain Stephen Carr has called time on his football career after making over 400 appearances for Tottenham, Newcastle and the Blues.
The former Republic of Ireland international, who also played 44 times for his country, made his professional debut as a Spurs player back in 1993.
"I am going on 37 and now is the time to bow out," Carr told the club's website.
Having spent the full 2012/13 season on the sidelines due to injury the veteran defender was realistic about his chances of playing again.
"I felt okay in pre-season but my knee just crumbled away - three operations in 18 months basically told me it had had enough. It just wasn't meant to be in the end," he added.