The head of the referendum commission, Frantisek Lipka, told reporters that 55.5 percent of voters favoured independence, exceeding the 55 percent threshold for the referendum to succeed.
The results will be deemed officially final on Saturday, after the expiry of the period during which they can be challenged.
The vote in the tiny Balkan state, wedged between the mountains and the sea and with a population of just 650,000 people, is the last nail in the coffin for the former Yugoslavia.
Following the referendum, Montenegro's parliament must declare independence
within 15 days of receiving the official results.
The European Union, which laid the groundwork for the plebiscite, promised to abide by the result.
Crucially, so too did Montenegro's neighbours.
A jubilant Prime Minister Milo Djukanovic said Montenegro's next target was to restart membership talks with the European Union and NATO.
Montenegro's integration, he told a press conference, "remains a strategic and national priority."
Mr Lipka, a Slovak diplomat, said that although the vote count was still to be finalised, the incoming results would not affect the final outcome, while the European security body OSCE described the vote as "free and fair."
Turnout was put at 86.3 percent, well above the 50 percent called for by the EU.
Recount demanded
Pro-Serbian parties Monday demanded a recount.
"Preliminary results of the referendum process should be rechecked and the ballots at all polling stations again recounted," said a statement from the opposition bloc.
They called for checks on the identity of voters at polling stations where there was a big increase in turnout.
However, two Serbian ministers said the will of the majority had to be respected, although an official response from Belgrade was not immediately forthcoming.
Serbia will maintain a "good neighbourhood relationship" with Montenegro, Finance Minister Mladjan Dinkic said.
Serbia must accept the result, said Rasim Ljajic, who is in charge of Belgrade's relations with the UN war crimes tribunal for the former Yugoslavia and is the federation's human rights minister.
"Most important is that the transition period is not painful, and that the two states continue their path toward the European Union and that there are no anti-Montenegrin feelings in Serbia, nor anti-Serb in Montenegro," he added.
Austrian Foreign Minister Ursula Plassnik, whose nation holds the rotating EU presidency, said the referendum was "an important European signal after the tragic developments which the Balkans had to live through during the 1990s."
OSCE chairman Karel de Grucht said the referendum had been "fair and free" and added: "The result reflects the will of the people."
"It is such a nice feeling when you have your own state," said Borko Savic, sipping a coffee in the sun in the Montenegrin capital Podgorica.
"Even more important is that everything passed peacefully."
Not everyone was so happy. "I can't believe this is happening. This is like separating meat from the bone," cried a woman selling newspapers, shaking her head in disbelief.
Analysts said Montenegro's independence drive would turn up the pressure to resolve the wrangle over Kosovo, the ethnic Albanian-dominated province which Serbs consider the birthplace of their national identity.
Tim Judah, a Balkans specialist at the Centre for European Reform based in London, said regional stability depended far more on Kosovo - "the final act in this 15-year drama" - than on Montenegro.
"Compared to Kosovo, Montenegro is easy," he said. "Kosovo is a much, much bigger problem."
The bloody wars of the 1990s had already led to Bosnia, Croatia, Macedonia and Slovenia leaving what was then Yugoslavia.
"We were witnesses yesterday of the end of the Yugoslavia project, started in 1918 with sincere intentions," Prime Minister Vlado Buckovski of Macedonia said.
The referendum was possible under the 2003 constitution which bound Serbia and Montenegro in a federation and contained an escape clause allowing either side to vote on independence after three years together.