Stocks ended higher after the Fed left interest rates unchanged and kept the "extended period" language in its statement.
Financials were the day's best performers, with JPMorgan and Bank of America leading the Dow.
Earlier, stocks had slipped into negative territory after the S&P downgraded its debt rating on Spain. This follows downgrades on Greece and Portugal, which sparked a selloff in the prior session.
The Dow gained 53.28, or 0.5 percent, to close at 11,045.27, after sliding more than 200 points on Tuesday.
The S&P 500 advanced 0.7 percent higher, while the Nasdaq finished flat.
The CBOE volatility index ended below 22 after surging more than 30 percent on Tuesday in its biggest one-day jump since October 2008.
The Federal Reserve said economic activity continues to strengthen and the labor market is beginning to improve but wasn't willing to remove that "extended period" language, referring to how long it intends to keep rates low.
As with past meetings, Kansas City Fed President Thomas Hoenig was the only dissenter, saying keeping that "extended period" language could create a buildup of future balances and limit the committee's ability to begin raising rates modestly.
"The Fed move was bullish for the market ... low rates are good for stocks," said Dave Rovelli, managing director of equity trading at Canaccord Addams. But, he cautioned, it won't last forever.
"If they [Fed policy makers] don't get their act together soon and start raising rates, it's not going to be too bullish," Rovelli said. "When we have all this debt to refinance the dollar keeps on weakening." he said.
Goldman Sachs shares continued to rise as investors shruggled off Tuesday's marathon Senate hearing grilling executives. While the market was a sea of red yesterday, Goldman was one of the only stocks that rose.
Banks bounced back from Tuesday's selloff, with Morgan Stanley , JPMorgan and Wells Fargo up more than 1 percent.
Republicans are also floating their first financial regulation reform counterproposal, after successfully blocking a bid to start debate on the existing Senate bill for the second straight day.
There will be short-term disruptions, but banks will “find another way to make money,” said Marc Pado, U.S. market strategist at Cantor Fitzgerald.
Pado added that while the Goldman Sachs hearing and the European debt downgrades may have pushed bank stocks lower yesterday, they were able to rebound because traders anticipate that financials are strong enough to weather such headwinds.
In today's economic news, mortgage applications fell last week as a drop in home refinancing volume outweighed the highest demand for home purchase loans in six months, according to the Mortgage Bankers Association.
Helping to asuage the market's concerns were details of a bailout plan for Greece.