Limbersky is currently with Czech second division side Viktoria Plzen, and has represented his country at Under-21 level and played in Serie A for Modena last season.
Arnesen said: "He already has experience in Italy and I look forward to seeing him develop here."
Meanwhile, Birmingham have turned down a "derisory" opening bid from Blackburn for Robbie Savage.
Reports suggest Rovers have offered to pay £500,000 up front and up to £2.2million overall for the Wales midfielder, depending on future success at staying in the Premiership.
But managing director Karren Brady said: "Blackburn faxed us an offer which was a waste of fax paper and a waste of my time reading it.
"I had told them not to bother putting a bid in writing unless it was a serious one. But what they came up with was nothing short of derisory.
"It could have meant us waiting five years to get our money. The way things are going all this could affect the relationship between the two clubs. They've got into Robbie Savage's head. But he's not for sale - and that's it."
