All 17 nations that use the euro will sign a treaty that allows a central European authority closer oversight of their budgets. Nine other EU nations are considering it. Britain is the sole holdout.
The Dow Jones industrial average rose 79 points, or 0.7 percent, to 12,076 in the first 15 minutes of trading. DuPont limited the Dow's gains, falling more than 6.6 percent after the company said it expects earnings this year will fall well short of Wall Street's expectations.
Bank stocks led the market higher. Morgan Stanley jumped 5.4 percent, Citigroup Inc. rose 2.8 percent.
The S&P 500 rose 9 points, or 0.8 percent, to 1,243. The Nasdaq rose 13, or 0.5 percent to 2,609.
The gains were broad. Of the S&P's 10 industry groups, only materials companies fell.
Earlier, stocks rose in Europe, though they were off their daily peaks. Germany's DAX rose 1.29 percent, France's CAC 40 1.4 percent.
Germany and France, the two biggest economies in the euro zone, had hoped to persuade all 27 members of the European Union to change an EU treaty and impose tight fiscal rules on its members. Britain refused to join in because it wanted to be exempt from proposed financial rules.
Many think the only path out of the debt crisis is a more active role by the European Central Bank, which could buy up more government debt to keep nations' borrowing costs down. It currently buys bonds in the markets, but only reluctantly, and in small quantities.
On Thursday the European Central Bank's president Mario Draghi suggested he had no intention of increasing bond purchases after the bank delivered on market expectations to reduce its main interest rate by a quarter percentage point to 1 percent.
Draghi said he was surprised by some interpretations of his comments last week that "additional steps" would be taken if the 17 countries that use the euro agreed to closer budget controls. Germany and France have proposed a plan on closer fiscal unity that will dominate debate at the EU summit of leaders, which starts later Thursday.
Earlier in Asia, stocks declined as traders responded to the deal with caution. Japan's Nikkei 225 closed down 1.5 percent, South Korea's Kospi sank 2 percent and Hong Kong's Hang Seng fell 2.7 percent.