Vucic, leader of the centre-right Serbian Progressive party (SNS), was given a mandate after a landslide victory in March elections called after Serbia began EU membership talks in the wake of a landmark accord with breakaway Kosovo last year.
Out of 228 deputies present at the SNS-dominated parliament, 198 MPs voted for Vucic's cabinet, 23 were against it and seven abstained.
"I am ready to undertake the implementation of reforms as I am convinced that if things remain the same, the consequences will be catastrophic," Vucic told parliament.
"The EU is not an ideal union, but it is the best union of the states that exists nowadays and we belong there," Vucic said.
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"If we work hard, I am convinced that Serbia can become an EU member by the end of this decade," he said.
Vucic will discuss the first moves of his cabinet with EU foreign policy chief Catherine Ashton, who will visit Belgrade tomorrow.
Vucic said he would personally lead Belgrade's delegation in the EU-sponsored talks with Pristina, expected to continue in coming weeks.
Serbia -- the largest country to emerge from the break-up of Yugoslavia in the 1990s, with a population of 7.2 million people -- has to reform antiquated labour and other economic laws and cut down on bureaucracy.
More than 20 per cent of the workforce is unemployed, and those with jobs struggle to survive on an average monthly salary of USD 480.