The announcement comes a week after France's ambassador to Niamey returned home under pressure from the regime.
"We will begin our disengagement operation this week, in good order, safely and in coordination with the Nigeriens," the military headquaters said.
President Emmanuel Macron had announced on Sept. 24 the withdrawal of 1,400 French troops "by the end of the year."
French soldiers were in Niger as part of a wider fight against jihadists across the Sahel region.
Some 400 are deployed alongside local troops in northwestern Niger, near its borders with Burkina Faso and Mali.
The "three borders" zone is known as a haven for the Islamic State group.
Soldiers withdrawing from the area would need cover to leave their exposed forward positions, the military said, possibly including air support from the larger force at an airbase outside the capital Niamey.
The troops have been living with uncertainty since the junta began demanding their departure, with irregular supplies of food and repeated anti-French demonstrations outside the Niamey base.
France had reinforced its presence in Niger after another coup-born military regime in Mali demanded its forces' departure, adding armored vehicles and helicopters to the drones and fighter jets already deployed.
Its troops will now have to withdraw either via Benin to the south or Chad to the east.
For now, Niamey forbids French flights over its territory.
Forum