He joined the club on a two-year deal under the Bosman ruling, having left Cardiff City at the end of the 2010/11 campaign.
The Glaswegian came through the ranks at Rangers and gained UEFA Champions League experience, as well as an SPL title and Scottish League Cup win, during a nine-year stay at his boyhood club.
Burke headed to South Wales in January 2009 and quickly became an integral part of a Cardiff side that came close to achieving promotion to the top flight on several occasions.
He had a tremendous first season at Blues, where he made 61 appearances, scored 14 goals and provided 18 assists to the cause. His efforts saw him sweep the board at the 2011/12 Player Awards Dinner, deservedly claiming the Players' Player of the Season, Player of the Season Award and Junior Blues' Player of the Season Award.
The club took up a one-year option on Burke in the summer of 2013, which runs until June 30, 2014.