North Korean State TV announced the 69-year-old ruler had died of a heart attack during a train trip on December 17.
Kim is believed to have suffered a stroke in 2008, but analysts say recent trips to China and Russia suggested his health had improved.
The leader, reputed to have had a taste for cigars, cognac and gourmet cuisine, was believed to have had diabetes and heart disease.
In Washington, the White House said it was monitoring events, and stated the United States remained "committed to stability" on the Korean peninsula. (RFE/RL).