Bosnian Petkovic, who spent a short spell at Switzerland's troubled Sion this year, is a surprise choice given he has never been involved in Italian football having spent most of his time managing an array of Swiss teams.
A short statement on Lazio's website confirmed his appointment but there were no details on the length of contract.
Rome's Lazio were almost relegated three seasons ago when Reja took over but he led the club into Europe the next term and in the season just finished they narrowly missed the Champions League spots by finishing fourth.
However, Reja had a rocky relationship with hard-nosed president Claudio Lotito and previously offered to resign before finally walking away last month.
Lazio captain Stefano Mauri was arrested last month on suspicion of match-fixing but the club have not been charged with any offence by the Italian federation.
The usual pre-season managerial merry-go-round in Italy is already in full swing with Pescara boss Zdenek Zeman set to take over at Lazio's city rivals Roma, the club he managed in the 1990s after a stint at Lazio.