Serbia won the green light on Friday to start negotiations by January on joining the European Union, capping a remarkable transformation in the prospects of the biggest former Yugoslav republic since the 1990s wars.

The decision, taken at an EU summit, rewards Belgrade for an April deal to improve relations with its former province of Kosovo, which broke away from Serbia in a 1998-99 guerrilla war.

EU leaders also agreed Brussels should launch negotiations with Kosovo on a so-called association agreement, which covers trade, economic and political relations and is a step on the path to eventual EU membership.

The leaders agreed talks would start in January 2014 "at the very latest" with Serbia, which was long treated as a pariah because of its central role in the wars that tore through the Balkans after the 1991 collapse of Yugoslavia.

"We are at a historic moment for the Balkans and for Europe as a whole," European Council President Herman Van Rompuy told a news conference, noting that the decisions on Serbia and Kosovo came as Croatia prepares to join the European Union on Monday.

"These ... decisions are an immediate result of the courageous agreement Belgrade and Pristina reached last April," said Van Rompuy, who will travel to both capitals on Monday.

Serbia and Kosovo have been at odds since Kosovo seceded in 2008 with Western backing. After months of EU-brokered talks, the two sides reached an agreement in April aimed at ending the virtual ethnic partition of Kosovo between its ethnic Albanian majority and a pocket of some 50,000 Serbs in the north.

The agreement still has to be fully implemented, and EU governments will assess progress before giving a final, formal go-ahead to talks later this year.

The EU negotiation process should help drive reforms in Serbia, the largest country to emerge from the former Yugoslavia, luring investors to its ailing economy.

Prime Minister Ivica Dacic, leader of the co-ruling Socialists and ex-spokesman for late Serbian strongman Slobodan Milosevic, said his government had worked hard for the EU bid.

"The date for (EU) accession talks is the first step of this great journey we are about to undertake," Dacic said in a live broadcast of a cabinet session.

Defence Minister Aleksandar Vucic, head of the conservative Serbian Progressive Party, said the Balkan state must do more to consummate reforms. "This is the turning point in our modern history. Serbia has demonstrated that no one can stop its way forward," Vucic told ministers.

In Belgrade about 2,000 hardline nationalists rallied peacefully against EU accession and demanded the resignation of the government.

CURRENCY BUOYED

The Serbian dinar swung upwards to 113.5 to the euro after the EU agreement from a low of 114.05 earlier in the day, currency traders in Belgrade said.

Mladen Dodig, head of research at Erste Bank in Serbia, said the date for EU membership talks would be a major support for reforms and improvement in the business climate, and would boost investor confidence and foreign investment.

"This will have a stabilising effect for financial markets and the foreign currency market, but I also expect structural reforms," said Miladin Kovacevic, the deputy head of the Serb Statistics Office.

NATO Secretary-General Anders Fogh Rasmussen welcomed the EU's decision and said KFOR, the NATO-ledKosovo peacekeeping force, would "continue to play its role by ensuring a safe and secure environment for all people in Kosovo". KFOR, in Kosovo since June 1999, comprises 5,000 troops from 31 countries.

Dacic said this week he hoped Serbia could wrap up membership talks in 4-5 years, although the widely held view in Brussels is that it is unlikely to be admitted before 2020.

In the past few years, Serbia has made notable strides towards the EU thanks to progress on democratic reforms and the capture of fugitives wanted for crimes during the Yugoslav wars.

Serbs consider Kosovo the fount of their nation and Orthodox Christian faith, but Belgrade lost control over the territory in 1999 when NATO conducted 11 weeks of air strikes to halt the killing and expulsion of ethnic Albanian civilians in a counter-insurgency campaign by Milosevic's security forces.

Kosovo is now recognised by 100 nations, including the United States and 22 of the EU's 27 members.

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Of Serbia's fellow ex-Yugoslav republics, Slovenia joined the EU in 2004, Croatia follows on Monday and tinyMontenegro began membership talks last year. Macedonia is a candidate, while Bosnia has yet to apply.

($1 = 0.7691 euros) (Additional reporting by Aleksandar Vasovic in Belgrade and Ethan Bilby in Brussels; Editing by Mark Heinrich)