The Fed’s two main tasks are helping to regulate the financial system and altering interest rates in response to economic growth and inflation. Regulating the financial system has become a much more important part of the Fed’s responsibilities in the wake of the financial crisis.

Many Democrats believe Ms. Yellen is likely to view Wall Street more skeptically than Mr. Summers, even though her views are closer to the centrist stance of the administration than to the positions of liberal Democrats on several regulatory issues. She is not, for example, a supporter of the push to break up large banks.

In the Senate, Republicans have frequently expressed concern that the Fed’s policies may destabilize financial markets and eventually accelerate inflation.Republican senators have typically threatened to filibuster major bills and nominations in recent years, suggesting Ms. Yellen may need 60 votes — including a handful of Republican votes — to be confirmed. A decade ago, Ms. Yellen was one of the first public officials to describe rising housing prices as a bubble that might pop, with damaging consequences for the broader economy. Still, as president of the San Francisco Fed, she did not translate her concerns into actions that might have prevented some of the worst effects of the bubble.

But in the aftermath of the resulting recession, she accurately predicted that the recovery would be painfully slow and that there was little reason to worry about inflation, a view that led her to press for the Fed to expand its efforts to revive the economy. No Federal Reserve chairman has been as deeply steeped in both the theory and practice of central banking as she is.

Mr. Bernanke also brought a distinguished academic history of having studied the Fed, but he spent only a few years as a Fed governor before becoming chairman. Ms. Yellen has spent more than half of the last 20 years as a top Fed official.

Until recently, she was telling friends that she did not expect to be nominated because Mr. Obama had made it clear that he wanted Mr. Summers for the Fed job. But when Mr. Summers withdrew his name on Sept. 15, Ms. Yellen became the front-runner by elimination.

As speculation swirled about the appointment, much of the debate revolved not around economic policy but gender. Mr. Summers, while he was president of Harvard, once wondered aloud whether inherent differences between men and women helped explain a lack of female science professors, causing some women’s groups to oppose his selection to lead the Fed. But within the White House, women were among his biggest supporters.