But unveiling the rescue package is not identical with "crisis over."
A potential sticking point: The deal arranged by EU finance ministers doesn't mean that parliaments in all member nations will ultimately agree to support those costs.
America's TARP fund, the Troubled Assets Relief Program of 2008, may be a cautionary tale. Even at the height of the financial crisis, America was wary of bailing out its own banking system. The initial congressional vote went against creating the $700 billion fund.
The eurozone package is politically more complicated. It's designed to show that 16 nations sharing the euro currency will stand united behind the debts of member nations to stave off a potential crisis of confidence that could damage them all.
"To disburse the money to actually fund this vehicle, it would require parliamentary approval" in participating nations, says Jay Bryson, a global economist at Wells Fargo Securities in Charlotte, N.C. "I'm cautiously optimistic that this crisis is over for now." But "there's still a long road ahead here."
Just like Congress with the TARP, European nations have a strong incentive to go along with the rescue. Failure to stem investors' worries, which sent stocks tumbling last week, could threaten the Continent's economic recovery.
Bailouts often aren't popular with voters however.
The deal by the numbers
The crisis fund would total €750 billion, with €440 billion coming from the nations in the currency union, an additional €60 billion from the wider European Union, plus €250 billion from the International Monetary Fund. Central banks are adding their own new liquidity programs sovereign-debt markets.
The German coalition government led by Chancellor Angela Merkel lost some electoral ground in a May 9 election, for example. And a separate bailout package for Greece, approved last week by the German parliament, was unpopular with many voters. Still, Ms. Merkel said she expects the parliament to consider the rescue package soon and to pass it.
"The euro zone's member states showed yesterday that we have a common political will to do everything for the stability of our common currency," Merkel said, according to an Associated Press report. "This is a determined and united message to those who think that they can weaken Europe."
As the largest economy in the eurozone, Germany would pay for more than one-fourth of the €440 billion fund.
Britain is not a member of the eurozone, and thus wasn't expecting to be drawn into this currency crisis. According to news reports Monday, Britain will oppose the planned €60 billion contribution by European Union members to the rescue fund. If some other EU nations joined in opposition, that money could be blocked.
The positive stock market reaction indicates that, for now at least, Europe's version of the TARP is expected to succeed.
Money might not be needed
But the rescue fund may also be tapped.
In fact, even if Greece and other debt-strapped nations follow through with fiscal austerity measures, that's no guarantee that the debt crisis will end. The austerity is expected to crimp economic output, making it hard to pay off their debts.
One alternative would be bailout money, to the degree that it's available. Another would be for Greece to opt out of the euro currency.
"Greece is essentially looking at a lost decade, given the austerity that its got to go through," Mr. Bryson says.