Stocks are closing at their highest level in more than eight months after the Federal Reserve pledged to keep interest rates near zero for three more years.
The Fed's monetary policy committee said it was unlikely to raise interest rates before late 2014. It had previously promised to keep rates low until mid-2013.
Stocks had been negative all morning, but turned positive on the news. Bond yields fell, indicating stronger demand.
The Dow closed up 83 points, or 0.7 percent, at 12,759. The S&P 500 closed up 11, or 0.9 percent, at 1,326. The Nasdaq closed up 32, or 1.1 percent, at 2,818.
More than three stocks rose for every one that fell on the New York Stock Exchange. Volume was heavier than average at 4.4 billion shares.