Nigerians make up the majority of undocumented migrants trying to make the treacherous crossing via the Mediterranean Sea to Europe.
Their repatriation began nearly a year ago but numbers have increased recently, with nearly 1,300 brought home in November, according to NEMA.
Another returnee, Omoburo, said he had been held in a Libyan detention camp for nearly nine months before he could return home.
"They used us to do all sort of things, to carry bombs, to carry ammunition, even to 'pack' dead bodies," he said as he stood in front of a large poster of Nigeria's first lady Aisha Buhari extending a warm "welcome" to the group.
The Nigerian ambassador in Libya has visited the camps for illegal migrants on their way to Europe, said Tiwatope Adeleye Elias-Fatile, spokesman for Abuja's ministry of foreign affairs.
The visits, made in partnership with the International Organisation for Migration, aim to identify detained Nigerians and issue them with emergency travel documents, he said on Monday.
"The embassy has a record of 2,778 registered Nigerians in accessible detention camps and they are ready for repatriation," the spokesman said, adding that 250 Nigerian migrants were being flown back to Lagos each week.
Once they have landed, they are taken back to their home towns or villages or given a small sum of money to make the journey on their own.
Libya's UN-backed government has hit back at growing criticism, saying that it was being overwhelmed by illegal immigration.