Mario Draghi, the head of the European Central Bank, was similarly optimistic.
"I'm actually quite pleased with the outcome of the European Council," said Draghi. "It showed the long-term commitment to the euro by all member states of the euro area. But also it reached tangible results in the shorter term."
He cited in particular the waiver of the ESM's preferred creditor status for Spain and the future possibility of using ESM for direct recapitalizing the banks, which is something the ECB had advocated for some time.
But he said strict conditionality was essential to the program's credibility.
Stocks around the world surged Friday, with markets in countries on the front line of the crisis doing particularly well. Italy's FTSE MIB and Spain's IBEX indexes rose 5.3 percent and 4.6 percent, respectively.
The euro was massively back in favor too, trading 2 percent higher at $1.2686.
Perhaps more importantly, the yield on Spain's 10-year bond dropped by 0.47 percentage points to 6.43 percent. Italy's was down by 0.25 percentage points to 5.83 percent. Both countries have seen their rates edge toward the 7 percent level which is seen as unsustainable over the long term.
The importance of recapitalizing banks directly from the bailout fund became evident this month when Spain was offered €100 billion ($125.6 billion) for its shaky banks.
Previously the bailout loan would have to be made to the Spanish government, which would lend it on to the banks. The prospect of having that debt on the government's books spooked investors, who began demanding higher interest rates to reflect the risk of a Spanish default.
"These steps are the obvious ones to take to try to restore some confidence in the market in the short term," said Gary Jenkins, managing director of Swordfish Research in London. "Alone, they do not solve the underlying problems but they might buy a bit of time, which is probably about the best they can do right now."
Though welcoming the measures that were taken, analysts think more will have to be done.
"If the aim is to ease tensions on the Italian and Spanish bond market on a more sustainable basis, we probably will need to have more assurance on the fire power," said analyst Carsten Brzeski of ING in a note.
Brzeski said more liquidity support from the ECB "looks inevitable" and may come as soon as Monday.
As well as trying to fix the euro, the EU leaders also agreed to devote €120 billion in stimulus to encourage growth and create jobs. Half of the total had already been earmarked and includes only €10 billion in actual new commitments. France had pushed for the growth package, arguing that austerity measures are stifling growth and making things worse.
They also agreed to give the ECB powers to oversee big European banks by the end of the year.
For the longer-term, the 27 leaders of the EU agreed on "four building blocks" of a tighter union — but postponed specifics until a study due in October. The building blocks, which include sharing debt in the form of jointly issued eurobonds, were laid out in a sweeping document presented by Van Rompuy and colleagues before the summit.
However, France's President Francois Hollande said the general agreement on the tighter union did not — for now — include any commitment on eurobonds from Germany and other stronger economies that have firmly opposed sharing debt with more profligate countries such as Greece.
Hollande claimed to play the role of mediator instead of partnering with Germany as France traditionally does.
"No one can say I won or I lost," he said. "What was at stake was Europe. That's who won."
Angela Charlton and Robert Wielaard in Brussels contributed to this report.