An EU police and justice mission to Kosovo has been agreed by all 27 member states within 24 hours of Serbia's presidential election coming to an end.
Nato's 16,000-strong force will continue working in Kosovo
No launch date has yet been given although that is likely to be decided by EU foreign ministers on 18 February.
The BBC's Oana Lungescu says the mission was approved in writing before a Monday deadline so as not to interfere with the polls in Serbia.
Kosovo is expected to declare independence in the next few weeks.
Hashim Thaci, prime minister of the breakaway Serbian province, 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.
The EU's 1,800 police and legal officials will take over from the United Nations in Kosovo, under UN Security Council resolution 1244, which refers to an international security presence.
The 16,000-strong Nato force will remain in Kosovo, which is a province of Serbia.
Kosovo's leadership has delayed proclaiming independence because of the second round of the presidential election, won on Sunday by Serbia's pro-Western President, Boris Tadic.
Serbia's electoral commission said Mr Tadic had secured 50.5% of the votes, defeating nationalist challenger Tomislav Nikolic, who polled 47.7%.
The election was seen as a referendum on Serbia's relations with Europe, with Mr Tadic promising EU-backed prosperity against Mr Nikolic's pro-Moscow campaign.
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.
"We wish to accelerate Serbia's progress towards the European Union."
The EU is due to sign an agreement with Serbia this week offering more trade, easier travel, and possible membership.
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."
"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."
Kosovo has been run by the UN since a US-led Nato bombing campaign drove out Serb forces accused of a brutal crackdown on ethnic Albanian separatists.
Cyprus and Romania said the EU civilian mission had to be approved after the election and before Kosovo declared independence because they would otherwise have a problem with the legal basis of the mission.
Both countries have already emphasised they will not recognise a unilateral declaration of independence.
As soon as a launch date is finalised, the EU will have 120 days to deploy its staff.
The BBC understands that the mission will be called EULEX Kosovo and will cost 205m euros for the first 16 months.
Sources say the EU has agreed to appoint Dutch diplomat Peter Feith as EU special representative to Kosovo.