Campaigning on a pro-Western reform ticket, Tadic won the presidential run-off vote on Sunday, defeating Tomislav Nikolic - an ally of former president Slobodan Milosevic.
The election results may signal a desire by Serbs to move closer to the EU and NATO - and away from the nationalist isolation of Milosevic's autocratic government.
Tadic received 53.7% of the vote, while Nikolic got 45% - with just under half of all voters turning out.
Although official results had not yet been announced, Nikolic's Serbian Radical Party conceded the defeat based on an independent election monitoring group's tally.
"That's the will of the people," said the Radicals' spokesman, Dragan Todorovic.
The election monitors expressed confidence in their count, saying the official results were unlikely to differ.
"It is certain that Boris Tadic has won and is the new president of Serbia," Zoran Lucic, the independent monitoring group (CeSID) spokesman.
The head of the European Commission Delegation to Serbia and Montenegro, Geoffrey Barrett, welcomed the result on Sunday.
"It is a very good result for Serbia and for democracy in Serbia. It has helped clarify the political scene ... we at the EU are very, very happy with this result."
EU said a Nikolic victory would
turn Serbia into a pariah state
Before the elections, EU leaders had told voters that a win for Tadic would help Serbia's European integration.
Fourth time lucky
Three previous attempts since 2002 to elect a president have failed because too few voters showed up at the polls.
This vote, however, was certain to produce a president because Parliament earlier this year scrapped a 50% turnout requirement for presidential elections.
Tadic, a 46-year-old Sarajevo-born psychologist and Belgrade college professor, entered politics in 1990 as a member of the pro-Western Democratic Party.
After the March 2003 assassination of Prime Minister Zoran Djindjic, Tadic was catapulted to the forefront - taking the party helm in February 2004.
He has been an ardent supporter of extraditing Serb war crimes suspects to the UN war tribunal in The Hague in the Netherlands.
Milosevic and others are standing trial on charges related to their roles in the Balkan wars in the 1990s - Europe's worst carnage since World War II.