About half the islands' population is registered to vote. The referendum will take place in the first half of next year, with international observers invited to verify the results. The date and wording of the referendum question will be announced in the next two weeks.
Gavin Short, chairman of the islands' legislative assembly, said: "I have no doubt that the people of the Falklands wish for the islands to remain a self-governing overseas territory of the United Kingdom. We certainly have no desire to be ruled by the government in Buenos Aires, a fact that is immediately obvious to anyone who has visited the islands and heard our views. But we are aware that not everybody is able to come to these beautiful islands and to see this reality for themselves.
"And the Argentine Government deploys misleading rhetoric that wrongly implies that we have no strong views or even that we are being held hostage by the UK military. This is simply absurd."
Downing St acknowledged that the Falklands Government had discussed its plans for a referendum with Britain, but insisted it had no role in prompting the decision.
Prime Minister David Cameron insisted that it was "absolutely right" that the islanders set out how they intended to "make their voices heard once more".
He added: "Next year's referendum will determine beyond doubt the views of the people of the Falklands. Britain will respect and defend their choice. We look to all UN members to live up to their responsibilities under the UN Charter and accept the islanders' decision about how they want to live."
There was no immediate reaction from Buenos Aires.
- Independent