Investor sentiment got a boost from better-than-expected earnings, a drop in oil prices as Hurricane Wilma bypassed oil and gas platforms in the US Gulf of Mexico, and speculation about bank take-overs.
Shares of American Express Co climbed 5.1 percent to $49.54 on the New York Stock Exchange and gave the biggest boost to the blue chip Dow average after the financial services provider's earnings beat expectations. The financial services sector was the Dow's top performer and among the best in the S&P 500.
President George W. Bush announced the nomination of Bernanke, who was a Fed governor until he became a top White House adviser last June, around 1700 GMT.
But the president's choice of Bernanke for Fed chairman was widely reported ahead of the announcement and the market quickly shot higher on the news.
The Dow Jones industrial average rose 169.78 points, or 1.66 percent, to end at 10,385.00. The Standard & Poor's 500 Index gained 19.79 points, or 1.68 percent, to finish at 1,199.38. The technology-laced Nasdaq Composite Index climbed 33.62 points, or 1.61 percent, to close at 2,115.83.
After the closing bell, shares of Texas Instruments Inc lost 3.4 percent to $29.87 on the Inet system after investors were disappointed by its fourth-quarter revenue forecast. Texas Instruments, the world's top maker of chips used in mobile phones, reported higher earnings and revenue.
Bernanke, 51, said following the nomination that, if confirmed, his "first priority will be to maintain continuity with the policies and policy strategies established during the Greenspan years." Greenspan, 79, is set to step down on January 31 after more than 18 years at the Fed's helm.
A Fed governor from 2002 until June 2005, Bernanke had been seen as the front-runner for the top Fed position. He is a long-time advocate of inflation targets, which would require the Fed to take certain actions if inflation reached some predetermined level.
The benchmark 10-year US Treasury note fell 15/32 to a price of 98-14/32, pushing its yield up to 4.45 percent from 4.38 percent late on Friday.
The Philadelphia KBW Bank Index, which includes the stocks of some of the largest US banks, rose 1.5 percent.
Some of the buying interest was tied to speculation over possible take-overs in the sector, said John O'Brien, head of sales trading at KeyBanc Capital.
Sovereign Bancorp Inc said on Monday it will acquire Brooklyn-based Independence Community Bank Corp for about $3.6 billion. Sovereign also said that Spain's Santander will become Sovereign's biggest shareholder by buying 90 million shares. That transaction whetted investors' appetite for the shares of other north-eastern US banks, such as Astoria Financial Corp, which rose nearly 8 percent to $28.49.