His son, Mahamat Idriss Deby Itmo, was named interim president by a transitional council of military officers, army spokesman Azem Bermendao Agouna said on state television.
Deby, 68, took power in a rebellion in 1990 and was one of Africa's longest-ruling leaders, surviving numerous coup attempts and rebellions. His death could deepen Chad's problems, and those of its allies.
On the domestic front, the military is divided and the opposition bridling against years of repressive rule.
Internationally, France and the United States will be hoping their counter-terrorism efforts are not now pushed off course. France said that it had lost "brave friend" and Chad "a great soldier".
He was killed just after he was declared winner of a presidential election that would have given him a sixth term in office. Most of the opposition boycotted the vote.