Private Nigerian airline Air Peace plans to operate two flights with Boeing 777 aircraft, the first leaving Lagos late on Tuesday to return on Wednesday with evacuees.
The plane can carry about 300 passengers.
President Muhammadu Buhari on Monday called for the immediate voluntary evacuation of all Nigerians wanting to return home, and Air Peace offered free flights last week.
"A private citizen who owns an airline has offered to evacuate Nigerians from South Africa who want to leave, and obviously there are immigration rules that go with that, so its a process," Ayanda Dlodlo, South Africa's Minister of State Security, told reporters in Cape Town.
Zimbabwe's Foreign Minister Sibusiso Moyo told reporters in the capital Harare that the government planned to evacuate 171 people from South Africa, including the bodies of two people.
Moyo added that Harare would "escalate" the evacuation if the situation deteriorated and he was seeking support from international organisations to help those affected.
In the latest outbreak of xenophobic violence in South Africa, deadly riots last week in Pretoria and Johannesburg killed at least 12 people including two foreigners, and targeted foreign-owned businesses.
The root causes of the latest series of attacks are unclear, although analysts suggest stubbornly high unemployment and grinding poverty were fuelling criminality.
In Katlehong, a township around 35 kilometres south east of commercial hub Johannesburg, 755 foreign nationals including 228 children are being cared for at community centres after fleeing violence.
"While there has been a significant decline in the number of incidents, police forces remain on high alert and are closely monitoring hotspots to ensure further violence does not erupt," Defence Minister Nosiviwe Mapisa-Nqakula said.
Police have arrested 653 people in connection with the attacks, mostly South African but including foreigners, police minister Bheki Cele said.
South Africa does not know how many undocumented foreigners are in the country of 58 million people. Democratic Republic of Congo, Bangladesh and Ethiopia topped the list of countries where people applied for asylum or refugee status in 2018.
Nigeria placed seventh with 948 people applying for refugee status and zero accepted, said Home Affairs Minister Aaron Motsoaledi.
Retaliatory attacks in Nigeria forced South African businesses to shut down for several days, and South Africa temporarily closed its embassy on safety fears.
Buhari will visit South Africa next month to address the attacks and seek a solution.
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