BRUSSELS — European leaders clinched a deal today they hope will mark a turning point in their two-year debt crisis, agreeing after a night of tense negotiations to have banks take bigger losses on Greece’s debts and to boost the region’s weapons against the market turmoil.

After months of dawdling and half-baked solutions, the leaders had been under immense pressure to finalize their plan to prevent the crisis from pushing Europe and much of the developed world back into recession and to protect their currency union from unraveling.

World stock markets surged higher today on the news. Oil prices rose above $92 per barrel while the euro gained strongly — a signal investors were relieved at the outcome.

The strategy unveiled after 10 hours of negotiations focused on three key points. These included a significant reduction in Greece’s debts, a shoring up of the continent’s banks, partially so they could sustain deeper losses on Greek bonds, and a reinforcement of a European bailout fund so it can serve as a $1.39 trillion firewall to prevent larger economies like Italy and Spain from being dragged into the crisis.

After several missed opportunities, hashing out a plan was a success for the 17-nation eurozone, but the strategy’s effectiveness will depend on the details, which will have to be finalized in the coming days and weeks.

The most difficult piece of the puzzle proved to be Greece, whose debts the leaders vowed to bring down to 120 percent of its GDP by 2020. Under current conditions, they would have ballooned to 180 percent.

To achieve that massive reduction, private creditors like banks will be asked to accept 50 percent losses on the bonds they hold. The challenge now will be to ensure that all private bondholders fall in line.