"This is the beginning of the reconstruction of state of institutions" and the return to rule of law, said General Najmi al-Nakoua, leader of the newly formed presidential guard.
The airport, located south of Tripoli, was badly damaged during fierce fighting in mid-2014, after which the Fajr Libya coalition of militias seized the capital and installed a government.
Flights in and out of Tripoli have been operating through Mitiga airport, formerly a military base east of the capital, that is under the control of the UN-backed Government of National Accord (GNA).
The airport had been controlled by forces loyal to Khalifa Ghweil, who headed a rival government and was dismissed after the formation of the GNA.
Ghweil, who has refused to give up his post, defiantly announced plans in February to reopen the airport and said that construction was underway.
On Friday, forces loyal to Ghweil tried but failed to retake positions they had lost in March, in fighting with GNA fighters that cost the lives of more than 50 people.
Since then, the rival forces gradually left their strongholds in the south of Tripoli, allowing the GNA to gain further ground in the capital.
General Nakoua said that besides the airport, "several barracks and military sites" were handed over to the GNA.
The presidential guard's mission was to protect state institutions, strategic facilities as well as members of the GNA, he said, without elaborating.
Libya has been wracked by chaos since the 2011 toppling of dictator Moamer Kadhafi, with rival militias and administrations vying for control of the oil-rich country.
A rival authority based in the country's east has also refused to recognise the GNA since it started working in Tripoli in March last year.
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