He said the assets of Landsbanki should be sufficient to cover all the deposits in Icesave, and the Icelandic government would provide help in raising funds if needed for the Icelandic compensation scheme.
"The government of Iceland is determined not to let the current financial crisis overshadow the long-standing friendship between Iceland and the UK," he said.
Banks dominate Iceland's economy, leaving the island of just 300,000 people heavily exposed to the global credit crisis.
The country has already nationalised two banks and its biggest bank, Kaupthing, was forced to take an emergency loan from Sweden on Wednesday.
Iceland's currency has plunged, and the Icelandic government was forced to abandon attempts to fix its exchange rate against the euro.
Analysts said it could take years for the the country to recover.
British saver Mike Davis, 62, who has £75,000 in retirement savings locked up in an Icesave account and said he had not slept for days, said he was "highly relieved and thankful" after hearing the chancellor's pledge.
"It has restored my faith in Britain and the British government," he said.
"It appears the chancellor is concerned about ordinary savers and ordinary families as well as saving the banks."
Another Icesave customer, Emma Durnford, 40, said: "After 24 hours of worry, stress and no sleep, it was really, really reassuring to see the chancellor's announcement this morning.
"I feel a lot better about it from this time yesterday. We now need to see what the next steps are, how to get compensation. I rely on the interest from my savings for income."
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