The contract for the Tetra communication system was signed with EADS, jointly controlled by French and German interests, while the missile deal was signed with the MBDA company, the missiles affiliate of EADS, the source said.
The Milan is a portable, medium-range anti-tank weapon.
On Wednesday, the son of Libyan leader Muammar Gaddafi was quoted by Le Monde, the French newspaper, that France had agreed to sell anti-tank missiles to Libya as part of a broader military agreement.
Nicolas Sarkozy, the French President, agreed an accord on defence and signed a memorandum of understanding for a nuclear energy deal when he visited Tripoli last week, after helping to free foreign medics imprisoned in Libya.
But he has denied the release of the medics was secured by an arms agreement.
Answering questions from journalists on Wednesday as to what deal had been offered by France, he said: "None."
The European Union lifted an arms embargo on Libya in October 2004, but Gaddafi's son, Saif al-Islam, said the ban had effectively remained in place, blaming the Germans for putting the brakes on possible deals.
Sarkozy flew to Libya hours after helping to secure the release of six foreign medics held in jail for eight years for allegedly infecting Libyan children with HIV.