Du Pont was found just before 7 a.m. at the Laurel Highlands state prison near Somerset, state prisons spokeswoman Susan McNaughton said. He was pronounced dead a short time later at Somerset Community Hospital.
He was serving a 13- to 30-year prison sentence after being found guilty but mentally ill in David Schultz's death.
"He had had some illnesses so we are considering it natural," said McNaughton, noting that the county coroner would ultimately make the determination on the cause of death. Somerset County Coroner Wallace Miller said later Thursday he was still gathering information on the death and had no immediate comment.
Du Pont was the great-great-grandson of E.I. du Pont, the French-born industrialist who founded the chemical company, and one of hundreds of heirs to the family fortune.
In January 1996, he shot and killed Schultz, a 1984 gold medal winner who came to live and train at the state-of-the-art Foxcatcher National Training Center that du Pont had built on his 800-acre property in Newtown Square. After the shooting, du Pont barricaded himself inside his home for two days, but was taken into custody when he left his mansion to fix a boiler police had shut off.
"In many ways, John Du Pont died for me the day that he took my son's life," Schultz's father, Philip, told The Associated Press from his home in Palo Alto, Calif. "So the fact that he's officially gone, is almost a moot point. I did forgive the man for what he did. I never forgave the act."
At the time of his trial, du Pont was one of the wealthiest murder defendants in American history. The trial exposed his bizarre, paranoid behavior and his many delusions, from his body being inhabited by bugs to his being spied on.
Du Pont had a reputation for acting erratically, including once driving two new Lincoln Continentals into a pond on his property, one after the other. Wrestlers who had trained at Foxcatcher alleged du Pont pointed guns at them, drank too much and once kicked out a wrestler because he was black.
His lawyers contended du Pont was insane and suffered from paranoid schizophrenia. At his arraignment, he told the judge he was the Dalai Lama. Meanwhile, a psychiatrist testified at his trial that it was cocaine, not mental illness, that fueled his rampage.
Months later, nearby Villanova University removed du Pont's name from its basketball arena. The building had been named after him when he pledged $5 million for its construction, though he apparently never fully followed through on the funding.
Du Pont had founded a wrestling program at Villanova in 1986 and even named himself head coach. The program was dropped two years later after the NCAA began investigating reports that du Pont was flying wrestlers in his private plane and letting them stay at his mansion.
A former Villanova assistant coach, Andre Metzger, claimed in a 1988 lawsuit that he was fired after nine months because he refused to become du Pont's lover. The case was settled out of court.
Over the years, du Pont lost several appeals of his murder conviction, including one to the Supreme Court in 2000 in which he was represented by Harvard law professor Alan Dershowitz.
Du Pont had sought an acquittal on insanity grounds, and the appeal challenged the Pennsylvania law that allowed the jury to find him guilty of third-degree murder but mentally ill in 1997. It contended the legal standard for finding someone legally insane is the same as the one for finding him guilty but mentally ill. The justices rejected the challenge without comment.
Only last month, du Pont lost another appeal with the federal appeals court in Philadelphia. He had contended his trial counsel was ineffective. The court disagreed.
Du Pont was the youngest of four children. A woman who answered the phone at the home of one of his sisters hung up on a reporter Thursday.