The Dutchman replaces Sinisa Mihajlovic, who resigned after failing to lead his country to the World Cup in Brazil.
Ljubinko Drulovic took interim charge for four friendly matches this year, but has stepped aside to make way for the former Netherlands, Russia and Belgium coach.
Serbia have been drawn in Group I of Euro 2016 qualifying and will face Portugal, Denmark, Albania and Armenia for a spot in France.
With Serbia having featured in just three of a possible eight major tournaments since the turn of the millennium, Advocaat is dumbfounded by the nation's recent poor record and will not accept anything less than qualification for the next European Championship.
"I wonder how a country with so much football talent has never been in a big tournament," he told reporters.
"I've seen around 10 games, but I have already seen all I need to know about the team.
"There are some very talented players, but they have not qualified for a major tournament - this is something we have to try to change.
"Money was not a motivation for me, I want to make Serbia successful.
"We have only one target, and that is to qualify. That is the only option we have. (There are) no excuses when the quality is there.
"We have to show that we can do it."
Advocaat will begin his reign with a September friendly clash against France on home soil before Serbia's qualifying campaign begins with games against Armenia and Albania in October.