|A man takes part in a protest against rising electricity prices in Lagos in 2016|
Russian state-owned company Rosatom will build one in the south, the other in the centre, sources at the Nigeria Atomic Energy Commission told the BBC.
The deal's exact worth is unknown, although some reports suggest it is likely in the region of $20bn (£15bn).
It is one of a number that Rosatom has been eyeing on the continent.
Can Africa lead the way on renewable energy?The company is also involved in discussions in Ghana and South Africa.
An initial agreement with the latter to build a plant was ruled unlawful in a South African court earlier this year.
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.
According to World Bank figures, 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.
Corruption at all levels has left the country out of pocket, and producing a fraction of the energy its 180 million citizens need.
Construction of the new power plants is expected to begin in the next two years.