The UN's International Court of Justice (ICJ) ruled on Thursday that Kosovo broke no laws by declaring independence, disappointing Belgrade and exhilarating Pristina.
Court President Justice Hisashi Owada said that international law contains no "prohibition on declarations of independence".
Serbia, which aims to reverse the 2008 secession, had hoped for a different outcome and remained defiant. President Boris Tadic told the nation in a televised address that the ICJ decision was "hard for Serbia" but that his government will continue the diplomatic fight.
"The court avoided to take a stand on the core issue and has released the debate on that and all political implications in the ... UN," he said.
Serbian Foreign Minister Vuk Jeremic vowed to "never recognise Kosovo's independence".
Serbia had hoped for a ruling that would have discouraged more countries from recognising Kosovo, before initiating a debate in the UN General Assembly with the aim of pushing through a resolution calling for new talks on the status of what it still considers its province.
Thousands of Albanians drove around late on Thursday in Pristina waving flags in celebration, while in the Serb enclave of Mitrovica, in northern Kosovo, several hundred people gathered in a quiet protest against the ICJ ruling.
"We do not accept this. For us this is Serbia," one visibly shaken man told a B92 television reporter.
Backed by Russia, Serbia has managed to keep the number of countries recognising Kosovo at a relatively low 69, though that number includes major powers including the US, Germany, France and Britain.
Moscow criticised the ruling as "political" and a "typical example of double standards," the Interfax news agency reported, noting the refusal of the international community to recognise Russian-backed secessionists in Abkhasia, Georgia.
After the non-binding ICJ opinion, momentum is likely to swing against Serbia's position. Kosovo leaders immediately jumped on the pendulum.
Prime Minister Hashim Thaci declared the ruling a "historic victory".
Kosovo President Fatmir Sejdiu said: "Serbia got its reply from ICJ. Serbia should accept the independence of Kosovo. We hope to see Serbia now uses a different approach towards Kosovo."
In The Hague, Kosovo Foreign Minister Skender Hyseni said: "We now look forward to further recognitions of Kosovo. We call upon states that have delayed recognising ... Kosovo pending the (ICJ) opinion to move forward towards recognition."
The US, the staunchest supporter of Pristina's drive to independence and one of the first nations to recognise Kosovo, said it was time for Belgrade and Pristina to turn the page.
"Serbia and Kosovo are both friends and partners of the United States," US Secretary of State Hillary Rodham Clinton said.
"Now is the time for them to put aside their differences and move forward, working together constructively to resolve practical issues and improve the lives of the people of Kosovo, Serbia, and the region."
European Union foreign policy chief Catherine Ashton welcomed the ICJ opinion, saying it opens "a new phase" and urging Serbia and Kosovo to forge "good neighbourly relations". The futures of both peoples lie "in the European Union", she said.
The EU is ready to help "a process of dialogue between Pristina and Belgrade ... to promote cooperation, achieve progress on the path to Europe and improve the lives of the people," Ashton said.
Western diplomats are calling for talks between the neighbouring countries - not negotiations on the status of Kosovo, which is a closed issue for Pristina, Washington and 22 out of the 27 EU nations.
In Slovakia, one of the five EU countries that refuses to recognise Kosovo, Foreign Ministry spokesman Peter Stano told the DPA that the ruling will not change Bratislava's stance.
Following the ICJ verdict - which also said that Pristina's independence declaration did not breach the UN's 1999 resolution establishing a UN protectorate over Kosovo - Secretary General Ban Ki-moon called the two sides to launch "constructive dialogue" and urged "all sides to avoid any steps that could be seen as provocative and derail the dialogue".
Now with a vastly dominant Albanian majority, Kosovo had once been Serbia's heartland province, the cradle of its statehood and 13th-century site of the founding of its church.