The club had been in conversation with the duo’s representatives in recent months but both will now look to pastures new.
Serbian striker Zigic was signed from Spanish La Liga side Valencia in May 2010 by former Blues boss Alex McLeish .
After making his debut away at Sunderland at the start of the 2010/11 campaign, Zigic went on to make a total of 147 appearances for the club over the next four years and found the back of the net 36 times.
Somewhat of a talisman in crucial games, the 6ft 8in frontman scored the opener in Blues' 2-1 Carling Cup success against Arsenal in 2011. He also netted the first goal against Bolton Wanderers in Blues' famous fightback against the Trotters in the final Sky Bet Championship game of last season.
Scottish international Burke arrived at St. Andrew's in June 2011 as a free agent after being released by Cardiff City and his performances on the wing quickly endeared him to the Blues faithful.
He had a tremendous first season, 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.
During his Blues career he racked up 151 appearances and scored 28 goals.
Birmingham City FC would like to place on record their appreciation of Zigic and Burke and wish them well in the remainder of their careers.