BRUSSELS—Euro-zone leaders agreed Thursday on a new €109 billion ($157 billion) bailout for Greece and new steps to prevent its debt crisis from metastasizing across the Continent—in a plan expected to trigger the first debt default by a nation using the common currency.

The meeting also produced a stark and open-ended declaration: The wider euro zone is committed to financing countries that take bailouts—thus far, Greece, Ireland and Portugal—for as along as it takes them to regain access to private lenders.

The move is a bold bid by Europe's leaders to corral an 18-month-old debt crisis that is veering dangerously out of control. Markets stopped lending to Greece, then Ireland, then Portugal. Fearful that policy makers have no concrete strategy for shoring up the larger economies of Spain and Italy, investors have lately soured on them as well. After months of dithering, European leaders resolved that they had to stop the bleeding.

Still, it remains to be seen whether the tourniquet will hold. Even after the new plan, Greece will have a staggering load of debt.

Thursday's agreement was the fruit of several concessions. European Central Bank Jean-Claude Trichet lost a fight to prevent default. German Chancellor Angela Merkel pried open her reluctant nation's pocketbook to write another check and be on the hook for still more.