18 December 2011 Last updated at 23:26 ET
He suffered a stroke in 2008 and was absent from public view for months.
His designated successor is believed to be his third son, Kim Jong-un, who is thought to be in his late 20s.
North Korea's state-run news agency, KCNA, urged people to unite behind the younger Kim.
"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," the news agency said.
The announcement came in an emotional statement read out on national television.
The announcer, wearing black, said he had died of physical and mental over-work. A later report from KCNA said Mr Kim had had a heart attack.
South Korea's military has been put on alert following the announcement and its National Security Council is convening for an emergency meeting, Yonhap news agency reports. The White House said it was "closely monitoring" reports of the death.
Asian stock markets fell after the news was announced.
Mr Kim had been making preparations to further install his son as his successor - a process that many had expected to see significant consolidation in 2012.
Professor Lee Jung-hoon, professor of international relations at Yonsei University in Seoul, told the BBC that with the transition of power from father to son incomplete, Mr Kim's death could herald "very unstable times" in North Korea.
"We have to be very worried because whenever there is domestic instability North Korea likes to find an external situation to divert the attention away from that - including indulging in provocation."