The (Newcastle) News Journal reported no foul play was suspected in the death of the 61-year-old killer, who had a history of health problems.
The one-time legal counsel to Delaware Gov. Tom Carper was convicted in the 1996 shooting death of gubernatorial secretary Anne Marie Fahey. He was serving his sentence in solitary confinement at the state prison near Smyrna.
Capano was found unresponsive about 12:30 p.m. by a guard conducting a routine security check, a prison spokesman said.
An autopsy was to be performed to determine the cause of death.
"He probably had a heart attack," L. Vincent Ramunno, Capano's brother-in-law, said, noting Capano had recently told family members he might have had minor heart attacks and had undergone medical tests.
Ramunno said Capano had gained a lot of weight and was taking medications for various conditions, the newspaper said.
Capano, a 48-year-old married father of four at the time of the slaying, had dated Fahey, who was 20 years his junior, for three years and then killed her at his Wilmington home because she refused to resume their affair, prosecutors said. He put her body in a large cooler and then, with the help of his younger brother Gerard, dumped her body at sea, authorities said.
Her body was never found.
Capano claimed Fahey was killed accidentally by another of his mistresses, The Philadelphia Inquirer said. He was sentenced to death but the state Supreme Court later overturned it and in 2006 he was re-sentenced to life without parole.
The case drew national attention, inspiring at least four books, with one turned into a TV miniseries, the Inquirer said.