Fresh after offering several of his promising youngsters new deals, the Blues boss has looked to secure the services of the Scotland international for a further 12 months.
Burke will now be contracted to Blues until June 30, 2014.
Since moving to St. Andrew's from Cardiff City in July 2011, Burke has made a total of 105 appearances and scored an impressive 22 goals.
The popular 29-year-old's performances during the 2011/12 season saw him collect the club's Player of the Year award, as well as the Players' and Junior Blues' Player of the Year awards.
Stay tuned for further reaction to Burke's extended stay following Clark's pre-match media briefing this morning.
Further details regarding remaining players whose contracts are due to expire this season will be announced in due course and in any event will be prior to the Football League deadline of Saturday 18 May.