The European Union has said it wants to speed up Serbia's progress towards membership, following the re-election of pro-Western President Boris Tadic.
Mr Tadic wants to push forward his European integration agenda
He took slightly more than half the votes cast in a tight contest with nationalist Tomislav Nikolic.
Mr Tadic had campaigned on a ticket promising EU-backed prosperity against Mr Nikolic's pro-Moscow campaign.
Meanwhile the prime minister of the breakaway Serbian province of Kosovo says it is now ready for independence.
Hashim Thaci said Serbian voters had chosen the future rather than the past - but he said this made no difference to Kosovo itself.
Kosovo is expected to formally declare independence in the next few weeks, and Mr Thaci said consultations were being held with what he called Kosovo's international partners - the EU and the US - before announcing a date.
"Kosovo is ready, it's united, it's prepared to declare independence and we will take a decision very soon," he told the BBC.
Kosovo has been run by the UN since 1999, when a US-led Nato bombing campaign drove out Serb forces accused of a brutal crackdown on ethnic Albanian separatists.
The US and most of the EU members back the independence plan, while Serbia and Russia are strongly opposed to it.
Both candidates in the Serbian election argued against independence for Kosovo.
The EU is due to sign an agreement with Serbia this week offering more trade, easier travel, and possible membership.
But the BBC's Oana Lungescu - reporting from the Serbian capital, Belgrade - says Mr Tadic could deal a death blow to the governing coalition if he signs the deal, even though he could argue that the election has given him a mandate.
Prime Minister Vojislav Kostunica had said he would not support Mr Tadic in the election if he signed the deal while Brussels pressed on with plans to deploy a police and justice mission to Kosovo.
Mr Tadic described this as blackmail, and fought and won the election without his prime minister's support.
In a message to Mr Tadic, Jose Manuel Barroso, President of the European Commission - the EU's executive arm - said the result was "a victory for democracy in Serbia and for the European values we share".
He added: "Your victory comes at a critical moment for Serbia and for the western Balkans.
"I am confident that Serbia will continue to play a constructive role in facing up to current challenges and in ensuring stability in the region.
"We wish to accelerate Serbia's progress towards the European Union."
The US has also congratulated Mr Tadic, saying it wanted to build a productive relationship with Serbia.
"President Tadic promised voters a European future for Serbia," said state department spokesman Sean McCormack.
"We will work with President Tadic and Serbia to see that promise fulfilled and Serbia firmly on the path to European integration."
Serbia's electoral commission said Mr Tadic had secured 50.5% of the votes compared to Mr Nikolic's 47.7% in a closely monitored election. Monitors put turnout at about 67%.
The election was seen as a fundamental choice for the country, which has yet to fully shake off the isolation of the 1990s.
Early on Monday, addressing hundreds of cheering supporters from a window overlooking the main Terazije avenue in the Serbian capital Belgrade, Mr Tadic said: "Serbia has shown its great democratic potential."
He added: "I think we have proved both to Europe and everywhere else in the world what kind of democracy we have in Serbia.
"We give support today to our fellow people in Kosovo and show them that we will never let them down.
"We don't want bad things to come to anyone. We want peace, co-operation with all countries in the region, but we demand Serbia be respected."
Mr Nikolic admitted defeat and congratulated Mr Tadic, but added: "I will remain to be his tough opposition."
While the presidency is a largely ceremonial office, the president is commander-in-chief of the armed forces, a role which carries strong symbolic weight.