The news came a day after Deby, who came to power in a rebellion in 1990, won a sixth term, as per provisional election results released on Monday.
He said the council will be led by Deby's 37-year-old son, General Mahamat Idriss Deby Itno.
Army spokesman Azem Bermendao Agouna announced Deby's death on state television and radio, surrounded by military officers he referred to as the National Council of Transition.
Deby, 68, came to power in a rebellion in 1990 and was one of Africa's longest-ruling leaders. Due to their growing proximity to N'Djamena, and the possibility of violence in the city, non-essential USA government employees have been ordered to leave Chad by commercial aircraft.
General Mahamat Idriss Deby Itno will be replacing his father, Idriss Deby Itno, as head of a military council. Following the clashes, Chad's army said it had killed 300 rebels and quashed the offensive.
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Four tanks and several soldiers were stationed at the northern entrance of the Chadian capital N'Djamena Saturday evening, where military vehicles were continuing to drive towards the fighting, an AFP journalist said.
Despite criticism of his autocratic rule, Western nations consistently looked the other way as Deby's army became a key player in the fight against Boko Haram in the Lake Chad region and against Islamic extremists in the Sahel.
Chadian opposition leader Saleh Kebzabo told VOA's French to Africa service that he was surprised to learn of President Deby's death and called for talks to solve the country's issues.
French President Emmanuel Macron, seen with Deby in Pau, France, on January 13, has spearheaded an worldwide military and peacekeeping effort in the Sahel to try and maintain stability in the region. "I'd rather die than witness instability in Chad", he said.
Chad's government has been forced to cut back public spending in recent years because of the l ow price of oil, its main export, sparking labour strikes. In the election results announced on Monday, Deby claimed 79 per cent of the vote.
The exact circumstances of Mr Deby's death were not immediately clear.
In an attempt to quell dissent, Déby had legalised political parties in 1993, which opened the way to the first multi-party elections in the country's history three years later.