Ireland and Portugal are to be granted an extra seven years to pay back their emergency bailout loans.
The EU and the IMF bailed out the Republic of Ireland in 2010 and Portugal in 2011.
The eurozone agreed to the terms at a meeting of finance ministers in Dublin.
Meanwhile, the eurozone finance ministers also said a 10 billion euro ($13 billion) EU bailout loan for Cyprus was ready for approval by member states.
That could happen by the end of the month and, if the IMF also gives the go-ahead, the first bailout money could be released by mid-May.
The plan for Ireland and Portugal is intended to give the countries’ financial systems more time to recover from the debt crisis after their bailout loans run out.
Ireland’s bailout money will run out later this year, and Portugal’s will run out in 2014.
The Irish and Portuguese repayment extensions are expected to be backed by all 27 EU members, which includes those outside the eurozone, later on Friday.
Eurogroup President and Dutch Finance Minister, Jeroen Dijsselbloem, said the ministers in Dublin had commended Portugal on its success in implementing the bailout programme but “asked them to maintain the reform momentum despite the difficult economic and domestic conditions”.
He added: “Ireland is a living example that adjustment programmes do work, provided there is a strong ownership and genuine commitment to reforms.”
The deal could be seen as something of a reward “for good behavior”, but also as recognition that an austerity-first approach was not always the best option.
The extension is especially important for Portugal. When it received a 78 billion euro bailout two years ago, it pledged to take various measures in its budget to reduce public spending.
However, last week Portugal’s Constitutional Court ruled that several of these measures in the 2013 budget were unlawful.
If Portugal was to drop the measures because of this, it may not remain eligible for more funds under its bailout.
On Thursday, it emerged that Cyprus would need to raise an extra 6 billion euros to secure the 10 billion euro bailout from Brussels and the IMF.
While confirming that up to 10 billion euros in loans will be provided to Cyprus, the eurozone finance ministers also rejected reports that the country might be granted more financial assistance.