The 54-year-old Getty suffered a narcotics-induced stroke in 1981 that left him paralyzed and nearly blind, The Washington Post reported Tuesday.
His death occurred Saturday at his estate in Buckinghamshire.
The grandson of billionaire J. Paul Getty Sr., John Paul III spent much of his childhood with his divorced mother in Italy.
He disappeared July 10, 1973, at the age of 16 following a late night out, Britain's Independent reported.
Police initially thought it might be a hoax when his mother received a phone call saying he had been kidnapped. Later, it was learned the teen had been abducted by a criminal gang linked to the Mafia.
His tight-fisted grandfather refused the kidnappers' demand for $17 million.
"I have 14 other grandchildren and if I pay one penny now I'll have 14 kidnapped grandchildren," J. Paul Getty Sr. said.
The stalemate broke five months later when an Italian newspaper received a package containing a lock of young Getty's hair and a severed ear.
The boy was released after the kidnappers received $2.8 million in cash, the Post reported.
Getty is survived by his son Balthazar Getty, an actor.
Funeral arrangements had not been announced.