The Dow Jones industrial average shot up 153.56 points, or 1.14 percent, to end at 13,657.86. The Standard & Poor's 500 Index jumped 20.78 points, or 1.41 percent, to 1,497.49. The Nasdaq Composite Index climbed 51.38 points, or 2.01 percent, to 2,612.98.
The Nasdaq composite index rose 2 percent, led by Cisco, the world's largest maker of computer networking equipment. This marked the Nasdaq's best three-day percentage gain in a year.
Financial companies and homebuilders, which have been pummeled in recent weeks as the housing market faltered, shone amid comfort in the Fed's view that the economy was likely to keep growing despite turmoil in credit markets.
Shares of homebuilders, hurt by the housing sector's slowdown, jumped after luxury builder Toll Brothers Inc. (TOL) reported sales that exceeded analysts' forecasts when it released preliminary results Wednesday. A Dow Jones index of homebuilders' shares surged 6.6 percent.
The volatility that has marked recent sessions resurfaced in the last hour of trading on a rumor that Goldman Sachs would make an announcement after the closing bell. Goldman denied that any announcement was pending.
"It's a casino atmosphere dominated by short-term traders, both long and short, responding to the tape and assorted rumors against the background of high anxiety," said Michael Metz, chief investment strategist at Oppenheimer & Co. in New York.
The Nasdaq had its biggest one-day percentage advance in 10 months.
"I think today's market reflects a subsidence of anxiety ... We've got to face up to the problem of subprime spreading to the whole housing sector and its impact on consumer confidence, but it does not look like the whole system is going to collapse, and I think that was the message of the Fed," Metz said.
Shares of Cisco gained 6.7 percent to end at $31.68 after hitting $32.25, the highest level since early 2001. Late Tuesday, the company raised its revenue target and reported earnings that exceeded analysts' expectations. Cisco also was among the stocks giving the biggest lift to the Standard & Poor's 500 index.
The Fed said Tuesday that turmoil from the housing slump was squeezing credit for some, but it nevertheless believed the economy remained reasonably intact.
Among financials contributing to the market's gains were shares of Citigroup Inc.(CC), up 1.9 percent at $49.49, and American Express Co, up 4.2 percent at $62.96, both in New York Stock Exchange trading. American Express was the Dow's top gainer.
The S&P financial index was up 2.2 percent, although for the year so far, the index was off more than 5 percent.
Shares of American International Group , the world's largest insurer and a Dow component, were up 1.4 percent at $66.48. Its earnings were expected after the closing bell.
Toll Brothers' stock gained 6 percent to $24.33. The company said that based on preliminary results, its third-quarter home-building revenue fell 21 percent to about $1.21 billion. But that was above analysts' forecast.
Other tech shares advancing included Broadcom Corp after Nokia said it had tapped the chip maker to produce advanced chips for its phones. . Broadcom shares shot up 9.8 percent to $35.98 on the Nasdaq.
Trading was heavy on the NYSE, with about 2.6 billion shares changing hands, above last year's estimated daily average of 1.84 billion, while on Nasdaq, about 3.56 billion shares traded, well ahead of last year's daily average of 2.02 billion.
Advancing stocks outnumbered decliners by a ratio of about 8 to 3 on the NYSE and by 2 to 1 on Nasdaq.