Falkland islanders have voted overwhelmingly in favour of retaining their status as a British overseas territory.
Some 92% of the island's 1672 eligible voters turned out, and 99.8% voted to remain with Britain.
Only three people voted no.
Argentina - which fought a war over the islands in 1982 - described the poll as illegal.
It maintains the dispute with Britain over the islands, known in South America as the Malvinas, should be settled at the United Nations.
Dick Sawle, a member of the island's legislative assembly, said: "To get a 99% result on the 'yes' vote, with only three voting 'no', I think is an absolutely phenomenal result which will send out the strongest possible message to the rest of the world about our right to self-determination - a right that was fought for in 1982, and which we have honoured tonight."
Welcoming the result, UK Foreign Secretary William Hague said: "We have always been clear that we believe in the rights of the Falklands people to determine their own futures and to decide on the path they wish to take. It is only right that, in the 21st century, these rights are respected.
"All countries should accept the results of this referendum and support the Falkland islanders as they continue to develop their home and their economy. I wish them every success in doing so."
Ahead of the referendum, Argentine President Cristina Fernandez de Kirchner had said the inhabitants' wishes were not relevant in what is a territorial issue.
Election observers from different countries oversaw the vote, including representatives of Chile and Mexico - despite an Argentine request for Latin American countries not to take part.
Argentine forces invaded the Falkland Islands on 2 April 1982. The garrison of Royal Marines was overwhelmed and other British South Atlantic territories including South Georgia were also seized.
In two months of fighting, 255 British and about 650 Argentine servicemen were killed, along with three Falklands civilians, before Argentine forces surrendered.
