The Bosnian, who is currently in charge of Serie A side Lazio, moved to Switzerland as a 24-year-old player and coached six different Swiss clubs before moving to Italy last summer.
He will replace the retiring German coach Hitzfeld immediately after the World Cup finals in Brazil.
Petkovic told football.ch: "I am very proud. Proud that the Swiss Football Association has entrusted me with the first team from July 1.
"I am also proud to take charge of the great team from my second... no... make that my first home.
"I've spent 27 of 50 good years of life in Switzerland, which says enough about where I feel at home."
Monday's announcement could hasten Petkovic's departure from Lazio, with the Roman club's president Claudio Lotito considering making a coaching change to arrest an alarming slide down the Serie A table.
Petkovic has, however, vowed to complete his contract in the Italian capital while Switzerland prepare for a World Cup campaign which pits them against France, Ecuador and Honduras at the group stage.
Fifty-year-old Petkovic will leave veteran boss Hitzfeld to that task for now but he admits he is excited about enjoying success with his adopted country in the future.
"I will do my utmost to ensure that Ottmar and his players can tackle the World Cup in as calm and as focused a way as possible," he added.
"I want to concentrate on my work now and then on July 1, 2014 I'll be fully ready for my new job.
"We will need to be ready immediately because our first assignment will be a qualifying match for the 2016 European Championships.
"I am convinced we can be successful in qualifying and also at the finals in France."
Petkovic has worked for Malcantone, Lugano, Young Boys, Bellinzona and Sion in Switzerland - he has also spent time with Turkish club Samsunspor - and guided Lazio to Coppa Italia victory over fierce rivals Roma in May.
On speculation he is set to lose his job at Lazio, he added: "These stories have been circulating for weeks, since someone made it public that I was a candidate to succeed Ottmar Hitzfeld.
"Such rumours and stories do not make life any easier but they seem to belong to the business. Above all, they do not change the fact that we pursuing our goals at the club undeterred.
"I would never neglect my current work in favour of a new job."
Hitzfeld, meanwhile, is calling time on a career that most notably saw him win five Bundesliga titles and the Champions League with Bayern Munich.
Since taking charge of Switzerland in 2008, he has led the landlocked nation to two World Cups.