European trading was buoyant from the outset. Britain's FTSE climbed 2.8 percent to 5,707.13. Germany's DAX jumped 5 percent to 6,324 and France's CAC-40 gained 5.9 percent to 3,362. Wall Street also surged at the open, with the Dow Jones industrial average rising 2.3 percent to 12,138 and the broader Standard & Poor's index gaining 2.5 percent to 1,272.
The Greek market rallied on hopes the early morning deal would finally lift the specter of government bankruptcy.
By the end of Thursday, shares on the Athens Stock Exchange had gained 4.8 percent to 811, with banking stocks up 12 percent - after suffering heavy losses earlier this week.
The hard-fought European deal asks banks to take on 50 percent losses on Greeks bonds. Eurozone countries and the International Monetary Fund will also provide an additional euro100 billion ($140 billion) in rescue loans as a second bailout package for Greece.
EU leaders "stopped the hemorrhaging," said Marc Touati, chief economist at Assya Compagnie Financiere in Paris. "(They) have saved the Eurozone and that's the good news and that's why the markets are reacting positively."
European leaders agreed early Thursday on a plan to provide Greece with more rescue loans to help relieve its crushing debt obligations. It will involve private investors taking bigger losses on the value of their Greek bonds, which would make Greece the first nation that uses the euro currency to be rated in default on its debt.
European Union President Herman Van Rompuy said the deal will reduce Greece's debt to 120 percent of its gross domestic product in 2020. Under current conditions, it would have grown to 180 percent.
In addition, the euro440 billion European Financial Stability Facility will be used to insure part of the potential losses on the debt of wobbly countries like Italy and Spain, rendering its firepower equivalent to around euro1 trillion ($1.4 trillion).
Loose ends still need to be worked out, and the fundamental problem of low economic growth in the eurozone has not been resolved by the crisis summit, some economists warned. "(They) have only saved it temporarily," Touati said.
"Unfortunately the fundamental problem concerning the absence of growth has not been resolved."
The world had been watching Europe Wednesday for a quick response, amid concerns that its debt crisis would drag down growth globally. So the response provided relief worldwide, as did strong data from the U.S.
Washington reported Thursday that the economy grew at a 2.5 percent annual rate from July through September on stronger consumer spending and business investment. That was nearly double the 1.3 percent growth in the previous quarter.
Shares in Asia posted solid gains earlier in the day. Japan's Nikkei 225 index rose 2 percent to close at an eight-week high of 8,926.54. South Korea's Kospi added 1.5 percent to 1,922.04. Hong Kong's Hang Seng gained 3.3 percent to 19,688.70.
Australia's S&P/ASX 200 jumped 2.5 percent to 4,348.20 after trading resumed following a 4-hour technical glitch.
Benchmark crude for December delivery was up $2.76 at $92.99 a barrel in electronic trading on the New York Mercantile Exchange.
Brent crude was up $2.80 at $111.69 a barrel on the ICE Futures Exchange in London.
In currencies, the euro climbed to $1.4172 from $1.3908 late Wednesday in New York.
