If confirmed by the Senate, Sotomayor, 54, would succeed retiring Justice David Souter. Two officials described Obama's decision on condition of anonymity because no formal announcement had been made.
Administration officials say Sotomayor would bring more judicial experience to the Supreme Court than any justice confirmed in the past 70 years.
A formal announcement was expected at midmorning.
Obama had said publicly he wanted a justice who combined intellect and empathy—the ability to understand the troubles of everyday Americans.
Democrats hold a large majority in the Senate, and barring the unexpected, Sotomayor's confirmation should be assured.
If approved, she would join Justice Ruth Bader Ginsburg as the second woman on the current court.