The newspaper said Tuesday the president could announce as early as Wednesday he will nominate Yellen to succeed Ben Bernanke, who is to leave office when his term expires in January.
Yellen, an economist and professor who is vice chairwoman of the Board of Governors of the Federal Reserve System, became the top contender to lead the Fed after former Obama economic adviser Lawrence Summers withdrew his name from contention in September because of criticism from Senate Democrats.
Yellen's nomination would require Senate confirmation, and with a government shutdown in place since Oct. 1, a timetable for hearings is far from certain, the Journal said.
Yellen is known to be a strong advocate of the Fed's easy monetary policy, and with inflation below 2 percent there is every reason to believe the Fed would keep its accommodative policies in place under her leadership, the newspaper said.
Yellen has been the No. 2 at the Fed since 2010 and 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. If confirmed, she would be the 15th person and first woman to hold the position.