The Senate voted 56-26 to approve Yellen, who becomes the 15th leader of the central bank.
President Obama said Yellen will be "a fierce champion" for the American people "who understands that the ultimate goal of economic and financial policymaking is to improve the lives, jobs and standard of living of American workers and their families."
"As one of our nation's most respected economists and a leading voice at the Fed for more than a decade -- and vice chair for the past three years -- Janet helped pull our economy out of recession and put us on the path of steady growth," Obama said in a statement issued by the White House. "Janet is committed to the Fed's dual mandate of keeping inflation in check while also addressing our most important economic challenge by reducing unemployment and creating jobs.
"And she understands that fostering a stable financial system will help the overall economy and protect consumers. I am confident that Janet will stand up for American workers, protect consumers, foster the stability of our financial system and help keep our economy growing for years to come."
About 15 minutes after the bipartisan vote, Sens. Jeanne Shaheen, D-N.H., and Elizabeth Warren, D-Mass., said they missed the vote because their plane was delayed returning to Washington. Both senators said they would have voted to support Yellen's nomination had they arrived in time.
In all, 17 senators were missing from the floor.
Bernanke's term ends at the end of the month.
Previously, Obama had praised Yellen's judgment, citing her early warning about the housing bubble and the recession.
Yellen, 67, is known as a strong advocate of the Fed's easy monetary policy, and with inflation at less than 2 percent she is expected to keep the Fed's accommodative policies in place under her leadership.
Yellen previously was president and chief executive officer of the Federal Reserve Bank of San Francisco and chairwoman of the White House Council of Economic Advisers under President Bill Clinton.
Yellen is married to George Akerlof, a Nobel prize-winning economist and professor emeritus at the University of California, Berkeley. Son Robert Akerlof is an assistant professor at the University of Warwick.