The 29-year-old joined Birmingham in a £6million deal from Valencia earlier this week.
Zigic has signed a four-year contract with the Blues.
“I am absolutely delighted to be at Birmingham. Playing in the Premier League is something I have always wanted to do,” he said.
“It will be a super experience and I’m thoroughly looking forward to it.
“I’ve been watching the Premier League for many years, it’s something I’ve always followed and kept up to date with.
“What really swayed me to join Birmingham was the potential of playing for such a big club in the Premier League and the potential of playing in Europe and it was an opportunity I couldn’t turn down.
“I am delighted to get the deal done so quickly.”
Birmingham managers Alex McLeish added: “He is certainly a big lad and I’m sure he could have a career in basketball.
“But despite his height he’s a good footballer, he brings other people into play and I spoke to Serbia coach Radi Antic and he said he was a fantastic team player.
“I’ve seen him for a number of years and spoken to some friends in Belgrade who knew him well and knew his character. Seeing what he did at Santander I hope he can do the same at Birmingham.
“I hope he has an outstanding World Cup and comes back injury-free.
“He is a well-known player in world football and I think he will do well at Birmingham.”
