Tadic garnered 50.57% against Nikolic's 47.71%, according to Serbian electoral authorities. The remaining votes were declared invalid.
During the inauguration ceremony, Tadic swore to do everything possible to preserve the sovereignty and territorial integrity of the Republic of Serbia.
"I swear to devote all my strength to the preservation of the sovereignty and territorial integrity of the Republic of Serbia, including Kosovo and Metohija," Tadic said.
The inauguration comes at a tense time for the Balkan nation, with its breakaway province of Kosovo set to unilaterally declare its independence this Sunday. Serbia has already ruled out the use of military intervention, however.
Although Kosovo's independence is backed by the United States and most EU countries, Serbia and Russia, among others, oppose the plans, considering any declaration a violation of international law.
Kosovo has been a UN protectorate since the NATO bombing of the former Yugoslavia ended a conflict between Albanian and Serb forces in 1999. Over 200,000 Serbians have left Kosovo since 1999 and some 100,000 are still living in the province, which has a total population of two million.