Electoral commission head Frantisek Lipka said that, according to complete preliminary results, 55.5 percent voted for Montenegro to become an independent state in the May 21 referendum.
That's just over the 55 percent threshold needed to approve the referendum under rules set by the European Union.
Parties that want to continue the union with Serbia have demanded a recount of the ballots.
However, Serbian President Boris Tadic said he accepted the result of the referendum and recognized the vote as an expression of the "free will" of Montenegro's citizens.
The European Union's Enlargement Commissioner, Olli Rehn, said the European Commission will recommend talks on closer ties with the new Balkan state, paving the way for it eventually to join the 25-member regional bloc.
Russia's Foreign Ministry also said it accepted the referendum results.
(compiled from agency reports)