Duncan, whose appointment is subject to Senate confirmation, said, "No issue is more pressing than education. . . . It is the civil rights issue of our generation."
Obama combined his announcement with a brief news conference in which he declined to say whether he supports the idea of a special election to fill the Senate seat he recently vacated.
Illinois Governor Rod Blagojevich has the power to make the appointment, but he was arrested last week and charged with, in effect, trying to enrich himself by appointing a new senator who could help him financially or politically.
Obama cut off a reporter who sought to ask a question about Representative Rahm Emanuel, the incoming White House chief of staff, who was reportedly heard on a federal wiretap talking with an aide to Blagojevich about potential Senate replacements. The president-elect said he has not been able to confirm that is the case.
Neither Obama nor Emanuel has been accused of any wrongdoing, and the president-elect has said he will announce the results of an internal investigation into the matter next week.
The appointment of Duncan left only a handful of Cabinet appointments yet to be made public, and in response to a question, Obama hinted broadly a Republican would be among them.
The posts yet to be filled include the secretaries of labor, transportation, agriculture, and interior, trade representative, and leaders for the intelligence agencies.
Senator Ken Salazar of Colorado, however, is expected to be named today as the chief at the Interior Department, and former Iowa governor Tom Vilsack is expected to be named agriculture secretary. Vilsack, from a major farm state, ran for president, but his campaign ended in February 2007, just as Obama's began, and he initially endorsed Hillary Clinton for the Democratic nomination.
So far, Defense Secretary Robert Gates, a holdover from the Bush administration, is the only Republican member of the incoming Cabinet.
Obama spoke of Duncan in glowing terms - they have been friends for years, live in the same Chicago neighborhood, and share a love of basketball as well as reformist instincts.
Duncan, 44, has run the country's third-biggest school district since 2001, pushing to boost teacher quality and to improve struggling schools and closing those that fail.
Duncan would take over a sprawling department that has focused during the Bush administration in winning passage and then implementing the president's signature No Child Left Behind education program. That effort has proved controversial, with supporters saying it is making progress in improving student skills, while local officials complain it focuses too much attention on standardized tests.
Obama said it was time for Washington to move beyond "tired debates" such as whether to approve the use of vouchers for students to attend private schools.
