The Fed's comments on the economy and its statement that it would keep interest rates low for an extended period lifted bank shares. JPMorgan Chase & Co rose 2.5 percent and BKW Bank index <.BKX> rose 1.4 percent.
Investors also scooped up shares beaten-down in Tuesday's selloff after debt downgrades for Greece and Portugal.
Worries about some euro zone nations' fiscal health have weighed on global markets for months. Some investors said the Fed had Europe's turmoil in mind when designing its policy statement.
The fact that the Fed is keeping rates low will be a relief for stocks, which have been in a trading range recently. said Subodh Kumar, chief investment strategist at Subodh Kumar & Associates in Toronto.
The downgrades in Europe are probably having an impact on the way the Fed is thinking. The risk is that they get frozen into their comments about extended periods since that's language they don't need.
The Dow Jones industrial average <.DJI> gained 53.28 points, or 0.48 percent, to 11,045.27. The Standard & Poor's 500 Index <.SPX> rose 7.65 points, or 0.65 percent, to 1,191.36. The Nasdaq Composite Index <.IXIC> added 0.26 points, or 0.01 percent, to 2,471.73.
The policymaking Federal Open Market Committee said in a statement after a two-day meeting, Economic activity has continued to strengthen and ... the labor market is beginning to improve.
That went some way to ease investors' concerns about events across the Atlantic when Standard & Poor's cut its credit rating on Spain by one notch, citing a more protracted period of sluggish growth than previously expected.
Energy and financial shares were the top gainers. Besides JPMorgan, which rose to $43.46, Exxon Mobil Corp added 1.4 percent to $69.19. Both were among top boosts to the Dow industrials.
Exxon also raised its second-quarter payout to 44 cents per share from 42 cents in the first quarter.
Earnings season stayed in high gear, with Dow Chemical Co up 5.9 percent to $31.83 after reporting a profit that beat expectations.
Comcast Corp , the No. 1 U.S. cable operator, posted slightly better than expected quarterly profit and strong cash flow growth, sending its shares up 1.9 percent to $18.81.
Broadcom Corp shares rose 1.7 percent to $35.41 a day after reporting a first-quarter profit, beating expectations, and giving an outlook above the consensus estimate.
Teva Pharmaceutical Industries continued to weigh on the Nasdaq after U.S. regulators warned the company about manufacturing violations at a California plant, according to a letter released on Tuesday. Teva's shares fell 1.7 percent to $58.66.
About 10.98 billion shares traded on the New York Stock Exchange, the American Stock Exchange and Nasdaq, below last year's estimated daily average of 9.65 billion.
On the New York Stock Exchange, about three shares rose for every two that fell, while on the Nasdaq, advancers beat decliners by a ratio of about 11 to 10.
(Reporting by Edward Krudy; Additional reporting by Ryan Vlastelica; Editing by Kenneth Barry)