Russian state-owned company Rosatom will build one in the south, the other in the central Nigeria. BBC reported.
The deal in Nigeria was reached after a long period of negotiation, with the two countries signing their first intergovernmental nuclear co-operation agreement in 2009.
Nigeria hopes the plants, which will initially be operated by Rosatom before they are handed over, will help deal with the country's energy deficit.
In Nigeria, the world bank report estimated more than 40% of the country was without mains electricity in 2014.
Nigeria is one of Africa's largest oil producers, but much of its oil wealth has been squandered over the years by the countries leaders and their foreign partners.