If confirmed by the US Senate, Yellen would replace Ben Bernanke, whose second four-year term as head of the Fed expires on Jan 31.
Obama is due to make the announcement at the White House at 3 p.m. EDT (1900 GMT), a White House official said on Tuesday. Bernanke is also scheduled to attend.
Yellen has been a forceful advocate of aggressive action to drive down unemployment and would provide continuity with the policies the Fed has established under Bernanke. Now her main challenge will be to steer policy back to a more normal footing and slowly wind down the extraordinary measures taken in the five years since the financial crisis.
The former professor has a long history in the top ranks of economic policymaking, including her service over the past three years as the Fed's No 2 official.
Yellen, 67, would have to oversee the tricky process of reversing the extraordinary stimulus the U.S. central bank put in place to shore up the world's largest economy, which eclipses Japan and China put together.
If she wins the Senate's backing, as expected, she would join the Fed's honor roll along with such household names as Paul Volcker and Alan Greenspan, predecessors as head of an institution that can influence the course of the world economy.
"She's an excellent choice and I believe she'll be confirmed by a wide margin," said Senator Charles Schumer, a Democrat from New York.
US stock index futures rose on the news.
"The market will be mildly pleased," said Matt McCormick, portfolio manager at Bahl & Gaynor Investment Counsel. "She uses the same playbook as Bernanke, and the market should not expect any change to the status quo."
Obama turned to Yellen after his former economic adviser Lawrence Summers withdrew from consideration amid fierce opposition from within the president's own Democratic Party, raising questions about his chances of congressional confirmation.