Yellen, 67, will replace Ben Bernanke, who is stepping down after serving as chairman for eight years dominated by the Great Recession and the Fed's efforts to combat it.
Senators confirmed her by 56-26, with numerous absences caused by airline flight delays forced by arctic temperatures around much of the country. All 45 voting Democrats were joined by 11 Republicans in supporting Yellen, while 26 Republicans voted "no."
Vice chair of the Fed since 2010, Yellen begins her four-year term as leader of the century-old bank on Feb. 1. With the economy rebounding from the depths of the recession but only modestly so far, many economists expect her to focus on how to nurture growth without putting it into overdrive, which could risk fueling inflation.
"The big debate will be when the Fed should tighten and how much, rather than when to step on the gas pedal and how hard," predicted Bill Cheney, chief economist for John Hancock Financial Services, who envisions a growing economy this year.
Under Bernanke, the Fed has driven short-term interest rates down to near zero and flushed money into the economy with huge bond purchases, which it has just started to ease. Yellen, a strong Bernanke ally, has supported those policies and is expected to continue them until concrete signs emerge of sustained improvement of the economy and job market.
A native of Brooklyn, N.Y., Yellen previously headed the Federal Reserve Bank of San Francisco, chaired President Bill Clinton's Council of Economic Advisers and has been an economics professor at the University of California at Berkeley.
Yellen, who as an academic has focused on unemployment and its causes, is considered a "dove" who wants the Fed more focused on creating jobs because unemployment is high and inflation is low. "Hawks" on these issues prefer a stronger emphasis on preventing inflation.
In brief debate on her nomination, Sen. Sherrod Brown, D-Ohio, lauded Yellen, who was one of the first to warn in 2007 of a housing bubble that could burst and damage the entire economy.
"She understands how risky financial practices deep inside the largest Wall Street banks can have a terrible and terrifying impact on American families," Brown said.
But Sen. Charles Grassley, R-Iowa, criticized Yellen for supporting the Fed's "easy money" policies of low interest rates and bond purchases.
"No one can deny that the risks are real and could be devastating" if those policies continue for too long, Grassley said.
Yellen's GOP critics have said the Fed has inflated stock and real estate prices by pumping money into the markets, creating investment bubbles that could burst and wound the economy anew.
Some also warn that as the Fed starts to trim its bond holdings, it could spook financial markets, threatening the economy's recovery by causing stock prices to drop and interest rates to rise.
Last month, the Fed announced that it will start gradually reducing its $85 billion in monthly bond purchases, trimming them back initially to $75 billion this month and taking "further measured steps" as economic conditions improve.
But the Fed also indicated that it will keep supporting an economy that it considers less than fully healthy. It said it will continue to keep interest rates low and try to boost unusually low inflation, which can slow spending and borrowing.
During her November confirmation hearing before the Senate Banking Committee, Yellen said the Fed's bond buying program has successfully supported the economy by keeping long-term borrowing rates low.
The Fed's holdings have reached $4 trillion, more than quadruple their level before the financial crisis hit in late 2008.
The U.S. economy has grown only modestly since the Great Recession officially ended in June 2009, though it has shown encouraging signs in recent months.
Unemployment fell to 7 percent last month, down from a recent peak of 10 percent in October 2009. The economy grew at an annual rate of 4.1 percent from July through September and has added an average 200,000 jobs monthly since August.
President Barack Obama nominated Yellen in October after considering selecting Lawrence Summers, a former Treasury secretary who had been a close Obama adviser early in his presidency. Summers withdrew after opponents complained about his temperament and past support for bank deregulation.
Obama called Yellen a "proven leader" and hailed her frequent focus on the unemployed, saying, "She understands the human cost when people can't find a job."
She will be the first Fed chair appointed by a Democratic president since Paul Volcker, who was appointed by President Jimmy Carter, left the post in 1987.
Yellen will preside over her first Fed meetings as chair on March 18 and 19.
AP Economics Writer Martin Crutsinger contributed to this report.