"It has all happened very quickly," he told the club's website. "I was preparing to play for Dinamo in the Champions League, but since then things have happened very fast and I'm very happy to be here.
"Every boy in Croatia dreams of playing in the Premier League and my dream has come true.
"I think the Premier League is in some ways better than the Champions League at times."
City boss Sven Goran Eriksson said: "He's a good defender, another good player first of all and that's the most important thing.
"He's young and the good thing with him is that he can play in different roles - centre half or right back. He's a tall, big guy and we look forward to him starting here, it's one more and I hope he will do very well for us.
"Vedran has plenty of international experience already at just 21 which is another plus for us."