President Barack Obama said Tuesday he plans to nominate a Harvard University finance professor and a private-equity executive to fill the two vacancies on the seven-member Federal Reserve Board.

The nominees are Jeremy Stein, 51 years old, a Ph.D. economist who did a five-month stint in the Treasury and White House early in the Obama administration, and Jerome Powell, 58, who was undersecretary of the Treasury for domestic finance under President George H.W. Bush.

If...