Falling crude oil prices lifted energy shares like Exxon Mobil Corp, which helped boost both the blue chip Dow average and the broad Standard & Poor's 500. Exxon Mobil was up 1.6 percent at $56.26 on the New York Stock Exchange.
According to a knowledgeable source, Bush was likely to pick Bernanke, 51, a Fed governor who became a top White House adviser last June, to succeed Greenspan, 79, as Fed chairman.
The mere mention of Bernanke for the Fed's top job, market analysts said, helped fuel some of the market's rally even before the official announcement later in the session. The announcement is expected to come at 1700 GMT.
"It's actually rallied a little on it. We have a couple sceptical folks here, but the market obviously likes it. The market's been a bit all over the map, but the last little run-up coincides with that rumour hitting the Street," said Rich Parker, head of trading at Stamford Group in New York.
The Dow Jones industrial average was up 109 points, or 1.07 percent, at 10,324.40. The Standard & Poor's 500 Index was up 12.52 points, or 1.06 percent, at 1,192.11. The technology-laced Nasdaq Composite Index was up 14.82 points, or 0.71 percent, at 2,097.03.
Chevron Corp's shares gained 1.5 percent to $57.16. ConocoPhillips advanced 2.1 percent to $59.35. Shares of Taser International Inc jumped 24.4 percent to $6.79 on Nasdaq after brokerage Jefferies & Co raised its investment rating on the beleaguered stun-gun maker's stock to "buy" from "hold."
On the losers board, shares of Cendant Corp fell almost 5 percent to $19.15 after the travel, hotels and real-estate services company said it would break itself up into four companies.
Consumer products maker Kimberly-Clark Corp shares rose 2.5 percent to $58.21. The company posted a 26 percent drop in quarterly profit, but still met Wall Street estimates on an operating basis, due to in part to price hikes on Huggies diapers.