Greece, the main source of the currency bloc's debt crisis, swapped its privately held bonds last week for new, longer maturity paper with less than half the nominal value, a move that cut its debt by more than €100 billion.
The exchange paved the way for eurozone ministers to give the final political go-ahead to a €130 billion package that aims to finance Athens until 2014. The decision will be formalised on Wednesday.
"As agreed, new official financing of €130 billion will be committed by the euro area and the IMF for the period 2012-2014," Jean-Claude Juncker, who chairs the Eurogroup of finance ministers, told a news conference.
Thanks to a high acceptance of the bond swap offer, Greece's debt would fall below a target of 120% of GDP in 2020, reaching 117%, from 160% now, he said.
As Greece's financial problems have lost some urgency, Spain has raised a new challenge. After announcing the previous government had missed its 2011 budget deficit target by a significant margin, the new administration said it would not meet the EU-agreed deficit goal for this year either.
Spain was supposed to cut its deficit to 4.4% of gross domestic product this year, but said it would only aim for 5.8% as it heads into recession. Its deficit in 2011 was 8.5%, far above a 6% goal.
In a statement, the Eurogroup said Spain should strive for a 5.3% deficit target this year, cutting it some slack from the initial goal but keeping the pressure on.
"The Spanish government expressed its readiness to consider this in the further budgetary process," it said.
The eurozone is keen that Spain, a far bigger economy than Greece which has so far avoided the need for a bailout, gives the financial markets no whiff of backsliding after Athens has been taken off the critical list, at least for now.
"It will be the responsibility of the Spanish authorities to choose the initiatives that will have to be taken in order to bring down the budgetary deficit in 2012, what is most important is what is the target for 2013," Juncker said.
"What is less important, but nevertheless important, are the avenues chosen in 2012."
Madrid pledged it would cut the deficit to 3% of GDP next year, in line with the agreed final deadline, but wanted the higher starting point and slower economic growth to be taken into account in determining the path in 2012.
"Spain's position is that two things have changed. The first: last year there was a deviation of 2.5% in the public deficit and the second: that the circumstances in terms of economic growth have changed significantly," Spanish Economy Minister Luis de Guindos said.
"Spain's commitment to the fiscal rules is absolute."
The European Commission expects Spain's economy to contract 1% this year after growth of 0.7% in 2011, a sharp downward revision from the last forecast for 0.7% growth.
Several other eurozone countries have committed themselves to meeting budget targets.
Belgium said at the weekend it was sticking to its deficit goals and came up with nearly €2 billion of extra spending cuts to make the target - a move that could add to pressure on Spain to stick to its agreed plan. Portugal and the Netherlands are also fixed on meeting their targets.
A stricter EU Stability and Growth Pact, which came into force in December, envisages fines for eurozone countries like Spain which are already running deficits above the 3% of GDP ceiling and missing their deficit reduction targets.