Investigators said a passer-by was walking near a wooded area near Duke's East Campus and saw what looked like a body.
Authorities found Charles Reddy, who had been reported missing on March 16. According to a missing persons Web site, he had a disorganized form of schizophrenia.
Police are trying to determine whether Reddy was off his medication.
Reddy was the son of Bill Reddy and Donna Slawson Kuniholm and stepson of Bruce Kuniholm and Isabel Reddy, Duke officials said. Bill Reddy is the William T. Laprade Professor of History and a professor of cultural anthropology; Donna Slawson Kuniholm is a visiting lecturer; and Bruce Kuniholm is director of Duke's Terry Sanford Institute of Public Policy.
Durham police say at this point, they do not suspect foul play.
"Bill Reddy and his wife Isabel Reddy and Donna Slawson Kuniholm and her husband Bruce Kuniholm are sad to confirm that their son, Charles Buell Reddy, was found dead today in a wooded area near East Campus," Duke officials said in a statement. "The cause of his death has not been determined, but Charles had been struggling with mental illness for the past few years. Family members are grateful for the expressions of sympathy they have received, and ask that their privacy be respected at this difficult time."