The official Korean Central News Agency (KCNA) said the leader “passed away from a great mental and physical strain” at 8:30 am on Saturday (2330 GMT Friday), while on a train for one of his “field guidance” tours.
It urged people to follow Kim’s youngest son and heir apparent Kim Jong-Un, who is aged in his late 20s.
“All party members, military men and the public should faithfully follow the leadership of comrade Kim Jong-Un and protect and further strengthen the unified front of the party, military and the public,” said the news agency and a weeping TV announcer.
KCNA said Kim died of a “severe myocardial infarction along with a heart attack”. It said an autopsy was performed Sunday.
The leader suffered a stroke in August 2008 which left him with impaired movement in his left arm and leg.
The North declared a period of national mourning from December 17 to 29.
South Korea’s government went on an emergency footing after the shock news, the South’s Yonhap news agency reported. It summoned a meeting of the National Security Council.
North and South Korea have remained technically at war since the three-year Korean conflict ended only in an armistice in 1953.