The 26-year-old midfielder signed on a Bosman free-transfer from Crystal Palace.
Blues boss Steve Bruce has been a big admirer of Kiroski ever since seeing him play in the Manchester United youth team that included Beckham, Scholes and Giggs.
United couldn't get a work permit for Kiroski and he moved on to Borussia Dortmund and then Sporting Lisbon before Bruce brought him back to England when he was manager at Crystal Palace.
"Jovan scored 20 goals in 21 reserve games when he was 18 at United," the Blues manager told the club's official website.
"And was there for four years but United couldn't get a work permit through for him.
"Jovan was among the Beckhams, Scholes and Giggs coming through at United - and Alex will tell you this - he was the pick of them all.
"I was intrigued to see how he got on after leaving Manchester.
"He played for Ottmar Hitzfield, one of the best coaches in the world at Borussia Dortmund and won the European Cup with them.
"At Sporting Lisbon I knew he wasn't very happy.
"They went through three or four coaches and he lost his way a bit.
"That's when I got him to Palace and that's when he gave up a hell of a lot of money to make that move last summer.
"In fact he put himself in a lot of jeopardy after what happened there with me, he showed me a lot of loyalty and I'm just so glad that we managed to get the Home Office's decision reversed."