Britain will "always be there" to defend the Falkland Islands, David Cameron has said, after 99.7% of the 1,513 residents voted to remain under British rule.
Cameron promised to defend the Falklands
Cameron said the result should "send a clear message" to Argentina.
He added: "It is the clearest possible result there could be.
"The Falkland Islands may be thousands of miles away but they are British through and through and that is how they want to
stay.
"People should know we will always be there to defend them."
"We believe in self-determination. 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."
Argentina considers the "Islas Malvinas" to be part of its national territory, taken from them by the British more than 180 years ago, and Kirchner took the issue to the United Nations (UN) on the 30th anniversary of the Falklands War last year.
In Argentina Senator Daniel Filmus, who is close to President Cristina Fernández de Kirchner, described the vote as a "publicity stunt".
"We must denounce this trickery that pretends to represent the popular participation of an implanted population," he said.
"This publicity stunt has no validity for international law."
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."
The islands' 2,563 residents did all they could in the lead up to the referendum to show their sympathies, waving Union Jack flags and dressing up in red, white and blue.
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 told the BBC.
Argentina considers the "Islas Malvinas" to be part of its national territory, taken from them by the British more than 180 years ago, and Kirchner took the issue to the United Nations (UN) on the 30th anniversary of the Falklands War last year.
Sawle said the Falklands government had been strengthened by the vote and would now take the referendum result to the UN this summer.
"We will see more authority being devolved to the Falkland Islands government," he said. "With this massive vote of the people behind us, this gives us this very clear mandate that we need for the future."
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.
"What this is all about is getting the rest of the world to realise what our neighbours are doing to us."
Journalist Celina Andreassi, from the Argentina Independent in Buenos Aires, said the strength of the Yes vote had been "quite predictable".
"The issue for most people here is that whether the territory is Argentine or British, not the people themselves," she said.
"I really don't think this referendum is going to make much of a difference... both sides are going to remain really strong in their position and we are probably going to continue where we are for a long, long time."
Shadow foreign secretary Douglas Alexander said: "The Falkland islanders have resisted overt and unhelpful pressure from the Argentinean government in the run-up to this referendum.
"However, they have now had the chance to put their views about their sovereignty firmly on the record.
"This referendum was a democratic process, overseen by international observers and has now made clear, once and for all, the view of the islanders."
In a message on Twitter, Labour leader Ed Miliband said: