The Fed said it would leave its lending rate intact and continue with its operation twist, which is a program of exchanging short-term securities for long term, which tends to keep long-term interest rates down.
Earlier, payroll company Automatic Data Processing Inc. said 110,000 jobs were added to the economy in October.
The figure is too small to nudge the 9.1 percent national unemployment rate lower but is still slightly higher than the 101,000 new jobs economists expected.
With the Dow Jones industrial average off more than 570 points in the first two trading sessions of the week, investors sought bargains and pushed the index up 178.08 points or 1.53 percent to 11,836.04.
By close of trading, the Standard & Poor's 500-stock index added 19.62 points or 1.61 percent to 1,237.90. The Nasdaq composite added 33.02 points or 1.27 percent to 2,639.98.
On the New York Stock Exchange, 2,529 stocks advanced and 508 declined on a volume of 3.9 billion shares traded.
On the Dow, financial companies did the trailblazing. Bank of America rose 5 percent while American Express gained 2.7 percent. JPMorgan Chase & Co. added 2.8 percent.
The benchmark 10-year treasury note rose 1/32 to yield 1.991 percent.
The euro rose to $1.3745 from Tuesday's $1.37. Against the yen, the dollar fell to 78.06 yen from Tuesday's 78.38 yen.
In Tokyo, the Nikkei 225 index shed 2.21 percent, 195.10, to 8,640.42.
In London, the FTSE 100 index rose 1.15 percent, 62.53, to 5,484.10.