Worries about Europe's debt crisis have been hanging over markets for weeks.
The Dow Jones industrial average rose 152 points, or 1.2 percent, to close at 12,724 Thursday.
The S&P 500 index rose 18 points, or 1.4 percent, to 1,344. The Nasdaq composite index rose 20 points, or 0.7 percent, to 2,834.
Four stocks rose for every one that fell on the New York Stock Exchange. Volume was higher than average at 4.4 billion shares.