Uefa’s annual congress voted by 28 votes to 24 to accept Kosovo’s application. Two votes were declared invalid.
The Kosovo president Hashim Thaci wrote on his Facebook page: “Kosovo in Uefa! The best news for countless fans in our republic. Now we will play in international championships, some games will be won some will be lost but no one will ever keep us out from green fields.”
Before the vote, the Serbian FA president Tomislav Karadzic had urged the Congress to reject the application, saying it was a case of politics interfering with sport.
“This is a political, not a footballing proposal,” he said. “We are facing a stern test, we must say no to politics, no to divisions that are maybe detrimental.
“It would create tumult in the region and open a Pandora’s box throughout Europe.”
Kosovo will apply next week to join Fifa and could play in the 2018 World Cup qualifiers if accepted.
Kosovo were granted permission two years ago to play friendly matches but with restrictions, which included a ban on displaying national symbols or playing national anthems at games.