The central bank is buying $85 billion of bond every month to keep interest rates low and encourage borrowing and spending. Low interest rates also keep bond prices high and push up demand for riskier assets like stocks.
Stocks rose strongly in the morning, then eased slightly in the early afternoon. The gains accelerated in the final hour of trading.
Boeing led the index higher with a gain of $2.73, or 2.7 percent, to $102.49. Industrial conglomerate 3M gained $2.44, or 2.2 percent, to $111.11. Twenty-six of the 30 stocks in the Dow rose.
Nine of the 10 industry groups in the S&P 500 index rose, led by consumer discretionarystocks, which stand to benefit more than other sectors if the economy picks up. Industrial companies and banks also posted strong gains.
The only S&P 500 industry group that fell was telecommunications, a so-called defensive sector that investors favor when they are seeking safety and high dividends.
Stocks slumped on Tuesday and Wednesday after disappointing reports on private-sector hiring and manufacturing. The S&P 500 index lost 1.9 percent over those two days. Friday's gain erased the S&P's loss for the week. The S&P gained 0.8 percent since last Friday.
Financial markets have turned volatile over the past two weeks as traders parse comments from Fed officials for hints about when the central bank will cut back on its support. When it happens, the wind-down will help nudge interest rates higher.
For investors who expect the Fed to stay the course, "these types of slow economic growth reports speak to that," said Kevin Mahn, chief investment officer at Hennion & Walsh Asset Management. "It keeps interest rates at record lows and it keeps the equity markets humming."