The EU would also have to approve the addition.
Despite a population of just 320,000 people, it seemed until last year that Iceland could thrive on its own, but it was badly hit by the global financial crisis which ultimately brought down the government.
The country's over-stretched banks collapsed under the weight of debt amassed during years of light regulation and many retailers went bankrupt.
The country's currency, the krona, has plummeted, while unemployment and inflation have spiraled.
The government was forced to resign and was replaced after a national election by a coalition of Sigurdardottir's pro-European Social Democrats and the Left Greens.
The disaster has forced Icelanders to consider seeking the shelter, and restrictions, of membership in the EU and possibly the euro currency, which it hopes will provide a more stable exchange rate and lower interest rates.
A Gallup poll in May showed 61.2 per cent of people in favour of EU talks and 29.6 per cent against.
But those polled were evenly split over the issue of actual membership.
Dozens of anti-EU protestors gathered again outside of parliament on Thursday, banging on pots and sounding horns.
European Union officials are enthusiastic about Iceland's vote, and Jose Manuel Barroso, the European Commission president, said the decision "is a sign of the vitality of the European project and indicative of the hope that Europe represents".
Fredrik Reinfeldt, the Swedish prime minister, whose country currently holds the rotating EU presidency, said in a statement: "I welcome that the Icelandic parliament has now decided for itself to apply for EU membership."
Iceland is already part of the European Economic Area, a trading block that gives Icelanders the right to live and work in the EU while allowing the country to run its own agricultural, fishing and monetary policies.
Full EU membership will hit Iceland's fishing industry, one of the few sectors to have survived the financial crash and a symbol of national pride.
If Iceland joined the EU it would probably have to sign up to its common fisheries policy and allow other European fishermen access to its waters.