According to the Asahi Shimbun daily, his daughter found him collapsed outside their house on Monday and called the emergency services.
He later died of heart problems at a hospital in the northern city of Sado, according to the local government.
He deserted during a drunken night in 1965, crossing the heavily fortified border into North Korea from the South.
He said later he was scared of being sent to Vietnam and thought North Korea would send him home.
Instead, he spent 39 years in Pyongyang, where he taught English to spy cadets in his North Carolina drawl and played a Yankee villain in propaganda films.
In 1980, he married Hitomi Soga, who was kidnapped by North Korean agents in the Cold-War era.
She was allowed to leave North Korea for Japan in 2002 and Jenkins followed her two years later with their two Korean-born daughters.
The Japanese government granted him permanent residency and he lived in Soga’s hometown on Sado, a picturesque island in the Sea of Japan.
Soga said in a statement released by the city government on Tuesday she was “very surprised” by his death and “cannot think of anything.”
Sado mayor Motohiro Miura expressed condolences in a statement, saying that Jenkins “worked at a souvenir shop and contributed to local tourism.”
After heading to Japan, Jenkins was court-martialled by the US military for deserting but given only a 30-day confinement.
North Korean agents kidnapped Soga and a number of other ordinary Japanese citizens in the 1970s and 1980s in order to train its spies in the Japanese language and culture.
In 2002, North Korea admitted kidnapping 13 Japanese civilians but the government in Tokyo believes at least 17 were taken.
A month later, five including Soga were allowed to return to Japan. Pyongyang insists the other eight are dead but has not produced cast-iron evidence.
The issue sours already strained Japan-North Korea relations and Prime Minister Shinzo Abe often wears a blue ribbon to remind him of their abduction.
Last month, during a trip to Tokyo, US President Donald Trump met Soga and the now elderly families of those abducted.
There are strong suspicions in Japan that dozens of other citizens were also snatched by the North.
James Joseph Dresnok, the only US soldier known still to have been living in North Korea after defecting more than five decades ago, died in November 2016, his sons confirmed in August.