BRUSSELS—Serbia will start membership talks with the European Union next month, the bloc agreed Tuesday, as it rewarded Belgrade for its efforts to improve ties with former province Kosovo.

For Serbia's government, the decision is the culmination of an 18-month-long push to draw closer to the EU, a move many thought unlikely when nationalist-leaning President Tomislav Nikolic secured a surprise election victory in mid-2012. Mr. Nikolic, a former ally of Serbian strongman Slobodan Milosevic, was once a strong EU critic but quickly...