Its government has agreed to pay back the estimated 4bn euros (£3.4bn) the UK and Dutch governments spent reimbursing citizens who lost money in the collapse of Icesave.
Repayments will begin in 2016 and will be completed by 2046.
The terms of the agreement must now be approved by Iceland's parliament and president.
The UK Treasury welcomed the deal.
A Treasury spokesman said: “The UK welcomes this new proposal from Iceland on IceSave and looks forward to successfully resolving the issue by signing a new loan agreement. Mutually-satisfactory closure of this issue will mark a new chapter in UK-Iceland relations.”