"Prime Minister Saad Hariri was informed of the French decision to supply the army with 100 ... HOT missiles that will be used by the military's Gazelle helicopters," the official told AFP.
"The missiles will be delivered before the end of February and are being given with no conditions attached," the official added.
In Paris, the office of French Prime Minister Francois Fillon confirmed that a letter to that effect had been sent to Hariri.
In August, a US lawmaker objected to the transfer saying the missiles could end up being used against Israel given the influence of the powerful militant group Hezbollah in Lebanon.
"The influence of Hezbollah militants and their Iranian and Syrian backers in the Lebanese government is rising," Representative Ileana Ros-Lehtinen, the ranking Republican on the House Foreign Affairs Committee, had said.
"Therefore, to sell weapons to Lebanon at this time would be very irresponsible and could jeopardize security and stability in the region," she said.
Local press reports had said Israel, which fought a devastating war with Hezbollah in 2006, also expressed concerns.
In November, Washington lifted a hold it had placed on 100 million dollars in military aid to Lebanon after receiving assurances that the army would closely monitor the border with Israel and that the assistance would not be diverted to Hezbollah.
Hezbollah is considered the most powerful military and political force in Lebanon. Intelligence officials estimate Hezoballah has amassed an arsenal of more than 40,000 short and long-range rockets as well as other sophisticated weapons, including anti-aircraft guns that the party claims can reach deep inside Israel.