The 67-year old Yellen, the current vice chairman of the Fed, would become the first female leader of the central bank.
Yellen has been viewed as the favorite for the job since former Obama economic adviser Larry Summers withdrew his name from consideration in September.
Previously, Summers' candidacy had drawn an unusual amount of attention to the nomination process, which usually is a relatively muted affair. He was forced to exit when a number of Democratic senators, including members of the Senate Banking Committee that approves Fed nominations, announced that they would not support him.
Yellen is expected to face a much easier path to confirmation. A number of Democrats took the unusual step of endorsing her for the post as an alternative to Summers when he was rumored to be Obama's preferred pick.
Banking Committee Chairman Sen. Tim Johnson, D-S.D., said Tuesday night that Yellen "has a depth of experience that is second to none, and I have no doubt she will be an excellent Federal Reserve chairman."
Senate Republicans are not likely to warm to Yellen.
“I voted against Vice Chairman Yellen’s original nomination to the Fed in 2010 because of her dovish views on monetary policy," said Sen. Bob Corker, a member of the banking committee. "We will closely examine her record since that time, but I am not aware of anything that demonstrates her views have changed,” Corker told the Washington Examiner.
Nevertheless, Republican-aligned economists have voiced support for Yellen, suggesting that she is as good a nominee as they can expect from Obama.
Yellen, who has served as Bernanke's number two for the past three years and has been on hand for all the major policy decisions during that period, likely will not present a change in direction for the central bank. She is regarded as a key proponent of the Fed's efforts to boost the economy with large-scale bond purchases and low interest-rate policies in recent years.
She would take the job, however, in the middle of a major transition in monetary policy. The Fed is expected to move to begin scaling back its stimulus policies in the months ahead, perhaps as she would be taking office in February.
The broader economic situation also will prove unwelcoming for the next Fed chairman, who is tasked with keeping inflation steady and promoting full employment. Five years after the financial crisis, the weak economic recovery has left millions of residents looking for work.
Yellen would come to the job with as much experience in central banking as any previous chairman. In addition to serving as the Fed's vice chairman, she has been a member of the Board of Governors and the president of the Federal Reserve Bank of San Francisco. She met her husband, the Nobel Prize-winning economist George Akerlof, in a cafeteria at the Fed in the 1970s.
Yellen also has experience in politics. She served as a top economic adviser to President Bill Clinton from 1997 to '99. In between stints in top economic policy posts in Washington, she has taught economics at Berkeley.
Yellen's nomination creates a vacancy at the vice chairman position. With Bush appointee Elizabeth Duke having resigned in August and governor Sarah Bloom Raskin slated to join the Treasury Department, three spots on the Fed's board will be left open. In filling those roles, Obama will have an opportunity to reshape the nation's monetary policy.