Both Yellen and Bernanke are scheduled to appear with Obama at the White House on Wednesday for a formal announcement.
Bernanke's term ends in January, completing a remarkable eight-year tenure in which he helped pull the U.S. economy out of the worst financial crisis and recession since the 1930s.
Under Bernanke's leadership, the Fed created extraordinary programs after the financial crisis erupted in 2008. It lent money to banks after credit markets froze, cut its key short-term interest rate to near zero and bought trillions in bonds to lower long-term borrowing rates.
Those programs are credited with helping save the U.S. banking system.
Yellen emerged as the leading candidate after Lawrence Summers, a former Treasury secretary whom Obama was thought to favor, withdrew from consideration last month in the face of rising opposition.
Yellen, 67, would likely continue steering Fed policy in the same direction as Bernanke. A close ally of the chairman, she has been a key architect of the Fed's efforts under Bernanke to keep interest rates near record lows to support the economy.
As vice chair since 2010, Yellen has helped manage both the Fed's traditional tool of short-term rates and the unconventional programs it launched to help sustain the economy after the financial crisis erupted in 2008. These include the Fed's monthly bond purchases and its guidance to investors about the likely direction of rates.
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