NEW YORK — A broad rally ended three days of losses in the stock market Wednesday as fears about Europe’s debt crisis ebbed.

Stocks rose sharply after a German court backed the country’s role in bailing out other European nations. The Dow Jones industrial average jumped 200 points in the first hour of trading and continued to climb throughout the day, ending up 275 points. The afternoon gains came after Italy’s Senate approved a deficit-cutting package and the Federal Reserve reported that U.S. business conditions are improving.

Traders also were speculating that President Obama would announce a $300 billion jobs package made up of tax cuts, state aid and infrastructure spending in an address to Congress tonight.

The Dow and other U.S. indexes had fallen in the previous three days because of worries over weakness in the U.S. job market and concerns that Europe’s debt woes could lead to a global economic recession.

“The market has been pricing in an out-and-out recession, so any hints that policy issues might be solved is a plus,” said Brian Gendreau, market strategist at Cetera Financial Group.

The Dow surged 275.56 points, or 2.5 percent, to close at 11,414.86. All 30 stocks in the Dow average rose.

The Standard and Poor’s 500 index jumped 33.38, or 2.9 percent, to 1,198.62. All 10 company groups that make up the S&P index rose. The Nasdaq composite shot up 75.11, or 3 percent, to 2,548.94.

The German court ruling also pushed the prices of Treasury securities lower as investors were more willing to hold risky assets like stocks. Treasury prices have been rising over the past week, sending their yields lower, as demand for lower-risk investments rose.

The yield on the 10-year Treasury note rose to 2.05 percent. Its price fell 50 cents per $100 invested.

“Market sentiment has actually been worse than economic data lately, and now you are seeing institutional investors saying, ‘I can get a better yield from the S&P 500 than I can from a 10-year Treasury’,” said Howard Ward, portfolio manager of the GAMCO Growth Fund.

Nine stocks rose for every one that fell on the New York Stock Exchange. Volume was below average at 3.9 billion shares.