In a statement, the Swiss Football Association said 50-year-old Petkovic would take the helm on July 1st, 2014.
He has been offered an initial 18-month contract, which will be extended through to July 2016 in the event that Switzerland qualify for Euro 2016, the SFA said.
Petkovic was born in communist-era Yugoslavia, where he started his playing career as an attacking midfielder before emigrating to Switzerland in 1987.
He plied his trade with clubs including FC Sion and Bellinzona, becoming the latter's player-manager in 1997.
He spent four stints at Bellinzona, in Switzerland's Italian-speaking Ticino region, leading them to promotion to the Swiss top flight and a cup final.
Petkovic has also managed Swiss clubs including Young Boys and Sion, and Turkish side Samsunspor.
In 2012 he joined Lazio in Serie A and guided then to the Italian cup final.
Hitzfeld announced in October he would be retiring from the game after the World Cup, at the age of 65.
The former Borussia Dortmund and Bayern Munich boss has been at Switzerland's helm since 2008 and has succeeded in taking them to their third World Cup in a row.
Unbeaten in the qualifiers -- albeit in a relatively easy group along with Iceland, Slovenia, Norway, Albania and Cyprus -- they jumped seven places to seventh in the FIFA rankings and were among the top seeds in the draw for the finals in Brazil.
They found themselves in Group E, along with Ecuador, France and Honduras.
"I've watched Switzerland and their development under Ottmar Hitzfeld closely. So I'm well aware of the challenges of succeeding him, while also knowing that I'll be taking over an established team with a bright future," Petkovic said in an SFA statement.
The choice of Petkovic -- born in the Bosnian capital Sarajevo and who defines himself as both Swiss and a Bosnian Croat -- has a symbolic edge given the make-up of today's squad.
Thanks to the SFA's admired youth development system, Hitzfeld developed a new generation of talent, often with roots in Switzerland's Balkan migrant community.
The talisman is 22-year-old winger Xherdan Shaqiri, who has ethnic-Albanian roots, and signed to Bayern in 2012 from Swiss powerhouses FC Basel.