Under terms of the agreement, EU bailout funds eventually will be injected directly into Spain's troubled financial institutions and it can remove the bailouts from its sovereign books, the Financial Times reported.
The change would occur after the eurozone establishes a single banking supervisor to be run by the European Central Bank.
Ministers meeting in Brussels also agreed to some concessions for Italy, creating conditions for it to become the sixth eurozone country to request EU assistance as part of the zone's debt crisis.
The alteration of the bailout rules came after Italy and Spain forced leaders blocked other agenda items to get a deal on short-term rescue measures, the Times said.
Ireland, which also is experiencing troubles in its banking sector, also would be considered for similar treatment, summit participants said.
Because countries no longer would be responsible for bailing out financial institutions on their own, bank failures such as those in Ireland and Spain would not burden national treasuries, ministers said, because the European Stability Mechanism would absorb the hits.
News of the breakthrough sent the euro 1.3 percent higher against the dollar to $1.2598, the euro's biggest daily gain in eight months.
Italian Prime Minister Mario Monti and Spanish Prime Minister and President Mariano Rajoy had asked for eurozone rescue funds and the European Central Bank to intervene more aggressively on financial markets to buy Spanish and Italian bonds, to ease the very high yields the two countries have been forced to pay on their sovereign debt.
Before the agreement was announced, German Chancellor Angela Merkel -- who rejected their pleas for immediate relief -- canceled her late-night news briefing after telling the 27 EU leaders such an approach threatened to derail the whole summit.
Dutch Prime Minister Mark Rutte, who supported Merkel, told reporters the only way Spain and Italy could emerge from the crisis was "to bite the bullet."
European Council President Herman Van Rompuy insisted Italy and Spain had not created gridlock.
"There are two countries who are very keen to make sure that there is an agreement, both on the long-term measures and on the short-term measures, but I wouldn't say there was any blockage," he said before the breakthrough was announced.
Notable deaths of 2014 [PHOTOS]