The actor was on hand to deliver a keynote address to the school's graduating students on Sunday, when he was presented with the honour by its president Amy Gutmann.
In his remarks to the students, Washington admitted that the idea of imparting wisdom to so many young adults was frightening.
"I had to come exactly because I might make a fool of myself," he joked. "I've found that nothing in life is worthwhile unless you take risks. Nothing."
The Academy Award winner also cautioned that the students should brace themselves for life's failure as well its successes.
He asked: "Do you have the guts to fail? If you don't fail, you're not even trying."
Washington's son Malcolm recently completed his sophomore year at the University of Pennsylvania and currently plays on the school's basketball team.
"The coach didn't give him enough playing time," Washington joked. "We'll talk about that later!"
The star will return to the big screen with Ryan Reynolds in the thriller Safe House, which is to be released on February 10, 2012 in the US and the UK.
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Watch Denzel Washington's commencement address below: