David Cameron has called on Argentina to respect the wishes of the people of the Falkland Islands to remain British.
The prime minister said the almost unanimous vote in favour of staying a British overseas territory was the "clearest possible result".
He said Argentina should take "careful note" of the referendum, and Britain would always defend the islands.
It follows pressure from Argentina over its claims to the islands, 31 years after the Falklands War with the UK.
Most Argentines regard the islands, which they call Las Malvinas, as Argentine and their recovery is enshrined in the national constitution.
Argentine President Cristina Fernandez de Kirchner has made clear that her country does not recognise the referendum, insisting it has no legal validity.
However, Mr Cameron said the islanders were entitled to the right of self-determination.
'Judge and jury'
Mr Cameron said: "The Falklands Islands may be thousands of miles away but they are British through and through, and that is how they want to stay, and people should know we will always be there to defend them.
"I think the most important thing about this result is that we believe in self-determination, and the Falkland Islanders have spoken so clearly about their future, and now other countries right across the world, I hope, will respect and revere this very, very clear result."
He added: "They want to remain British and that view should be respected by everybody, including by Argentina."
Labour's shadow foreign secretary Douglas Alexander said the islanders had resisted "overt and unhelpful pressure" from the Argentine government in the run-up to the referendum.
"This referendum was a democratic process, overseen by international observers, and has now made clear, once and for all, the view of the islanders," he said.
Writing in Clarin, a popular daily newspaper in Argentina, former cabinet chief Rodolfo Terragno said the people of the Falkland Islands had "proved Argentina right".
"Great Britain can no longer say the inhabitants of the Falklands are a third party in the Anglo-Argentine conflict. The islanders have confessed they are British," he wrote.
"They cannot decide which of the two countries is right. They would be judge and jury."
Nigel Haywood, governor of the Falkland Islands, said the referendum was a "massive demonstration of the way the Falkland Islanders feel and of the way they see their future".
"Obviously it is a major principle of the United Nations that a people have their right to self-determination, and you don't get a much clearer expression of the people's self-determination than such a large turnout and such a large Yes vote," he said.
Dick Sawle, a member of the Falklands Legislative Assembly, said the vote should send out "the strongest possible message to the rest of the world about our right to self-determination".
"The British government is 100% behind us and it will be our job now as a government to get that message out to the rest of the world and every country that will listen to us," he said.
Islander Lynda Buckland said the result was "absolutely brilliant".
"It sends a message out to the rest of the world that we are British and we want to remain that way. My family has been here since 1842 and that is longer than most Argentines have been in Argentina," she said.
Of 1,517 votes cast in the two-day referendum, just three votes were against. There was a turnout of more than 90% from 1,672 British citizens eligible to vote in a population of about 2,900.