Obama spoke to some 5,000 graduates and their families at the ceremony on the National Mall. She agreed to be their speaker after students, faculty and staff met her challenge to complete 100,000 hours of community service.
"I have one more request to make of you, one more challenge," Obama said. "Keep going. Keep giving. Keep engaging."
Graduates in black robes cheered as Obama spoke with the Capitol behind her.
"So many of today's challenges are borderless, from the economy to terrorism, to climate change ... you are uniquely equipped to solve those challenges," said Obama, who spoke for about 30 minutes.
Obama said that at her husband's inauguration, "he pledged to seek a new era of American engagement and he asked each of us to embrace anew our duties."
"Now I'm not a president. I'm just a citizen. But as a citizen I'm asking you as graduates of this global institution to seize those responsibilities gladly," she said. "I'm asking you to play your part."
Earlier this month the first lady gave a commencement speech at the University of Arkansas at Pine Bluff, a historically black college. Obama, who graduated from Princeton and Harvard Law School, will also speak next month at the graduation of Anacostia Senior High School in Washington, a public school she visited last year as part of her mentoring program for young women.
During the ceremony, George Washington University president Steven Knapp presented Obama with an honorary Doctor of Public Service degree. Pianist and composer Dave Brubeck and entrepreneur A. James Clark also received honorary degrees at the commencement.