The former Serbia. Yugoslavia, Internazionale, Lazio, Roma and Sampdoria defender, 43, was approved in a unanimous decision by the FSS executive committee.
Mihajlovic succeeds Vladimir Petrovic, who left his post by mutual consent after Serbia failed to qualify for Euro 2012.
They have since been managed by caretaker boss Radovan Curcic.
"I am completely confident we can reach the World Cup finals and I will step down if we fail," Mihajlovic told a news conference after signing a two-year deal.
"It's going to be a lot of hard work and we are also pressed for time because the qualifiers start in September whereas we have to inject fresh blood into the team and rebuild almost from scratch, but we have enough talent and potential.
"I had offers from three Italian clubs during the protracted talks with the FSS, which lasted for two and a half months, but was never in doubt because it is every coach's dream to take charge of his country's national team," he added.
A tough-tackling but skilful defender in his playing days, Mihajlovic has managed Fiorentina, Catania and Bologna since retiring in 2006.
Serbia have a tough 2014 World Cup qualifying group which contains three Balkan rivals - Croatia, Serbia and Macedonia - plus Wales, Scotland and Belgium.
"I will ask the FSS to make sure we play only in venues where fans will behave in order to stop tarnishing Serbia's reputation which is already blotted by a plethora of incidents," he said.
"The players, on the other hand, will have to sign a code of conduct binding each and every one who represents Serbia to learn the national anthem, behave at international and club level and put their hearts on the sleeve.
"Football should be entertainment for all fans who love the game, including women and children, while commitment, passion and patriotism must go hand in hand with a player's talent."
Mihajlovic has called up 31 players for Serbia's upcoming friendlies against European champions Spain this week, France on May 31 and Sweden on June 5.
His squad includes four debutants and is devoid of many stalwarts who endured a poor Euro 2012 qualifying campaign including Dejan Stankovic and Nemanja Vidic, who both retired from international football after the fiasco.
"I spoke to both of them and they confirmed that making a return to the national team was out of the question, although Stankovic will be with us in an advisory role whenever possible because of his vast experience," Mihajlovic said.
"The three games against teams taking part in Euro 2012 will show where we stand at the moment and what departments we need to address ahead of the World Cup qualifiers."