Dave Smith, 67, who drove for TV personalities including Savile in the 1980s, had been due to stand trial for allegedly abusing a 12-year-old boy in 1984.
After he failed to show up at the court hearing, a warrant was issued for his arrest.
When officers went to his home in Lewisham, South London, they discovered a body, The Telegraph reported.
"Police attended a private address as a man had failed to appear at Southwark Crown Court today. At approx 14:20 pm (local time) officers entered the address and found the body of a man. He was pronounced dead at the scene. Next of kin are being informed," a Scotland Yard spokesman said.
Smith faced two counts of indecent assault, two of indecency with a child, and one of buggery, all relating to the 12-year-old boy, between June 1 and July 21, 1984.
There are fears that he took his own life, the Sun reported.
During the hearing at Southwark Crown Court, Smith's defence counsel Sandy Canavan said her solicitor had been attempting to contact him without success.
"He has been regularly in contact, I am concerned at the lack of contact. He is the sole carer for his very aged and very unwell mother, that may have affected why he's not here today," she said.
The judge issued a bench warrant, backed for bail, with the condition that he surrender to the court by 9:30 tomorrow morning, with the case to be listed for 10 am (local time).
Smith was the first person to be charged under operation Yewtree, set up in the wake of hundreds of allegations of sexual abuse against Savile, who died in 2011 aged 84.
Scotland Yard has led the probe, and separated its inquiries into those involving Savile, those involving Savile and others, and those involving others.