The approval was disclosed by Zubairu Dada, Minister of State for Foreign Affairs.
Dada said the approval was given on Wednesday at the Federal Executive Council (FEC) meeting presided by Vice-President Yemi Osinbajo.
The minister said AirPeace and Max Air airlines have been selected to provide three aircraft to facilitate the evacuation of Nigerians.
Russia and Ukraine have been at war since last week over the latter’s decision to join NATO.
About 5,000 Nigerian students have been affected by the ongoing war in Eastern European countries.
The Nigerian government had expressed desires to evacuate its citizens in Ukraine.
Nigerian embassies in Romania, Hungary, and Poland have received over 256 stranded Nigerians from Ukraine.
Geoffrey Onyeama, the Minister of Foreign Affairs, had said the Federal Government would commence the evacuation of stranded Nigerians from Ukraine from Wednesday.