Tadic supporters poured on to the streets of Belgrade, the capital, to celebrate, sounding car horns and waving the blue and yellow flags of the Democratic Party.
Tadic wants closer ties with the EU.
The issue of Kosovo had weighed heavily in the elections, though both Tadic and Nikolic had opposed ethnic Albanians' independence drive.
The choice of Tadic is likely to mean Kosovo will wait for a few weeks, in deference to the EU's wishes, before declaring independence.
Kosovo's ethnic Albanian leaders had said they would set the date for their declaration of independence after the election result was announced.
Kosovo has been run by the UN since Nato drove out Serb forces in 1999 to halt ethnic cleansing during a counter-insurgency war.
Neither the EU nor the US has shown any sign of backing down over Kosovo's independence, despite warnings from Vladimir Putin, the Russian president, that he will never accept it.