The government and parliament have been dissolved. A curfew has also been imposed and the borders have been shut.
Déby, 68, spent more than three decades in power and was one of Africa's longest-serving leaders.
An army officer by training, he came to power in 1990 through an armed uprising. He was a long-time ally of France and other Western powers in the battle against jihadist groups in the Sahel region of Africa.
Déby "breathed his last defending the sovereign nation on the battlefield", an army general said on state TV on Tuesday.
He had gone to the front line, several hundred kilometres north of the capital N'Djamena, at the weekend to visit troops battling rebels belonging to a group calling itself Fact (the Front for Change and Concord in Chad).
A military council led by Déby's son, a 37-year-old four star general, will govern for the next 18 months.
Mahamat Idriss Déby Itno will lead the council but "free and democratic" elections will be held once the transition period is over, the army said in its statement.
Ahead of the election on 11 April, Déby campaigned on a platform of bringing peace and security to the region.
But there has been growing unhappiness over his government's management of Chad's oil resources. Source: BBC
