Sergei Kiriyenko, the head of Rosatom, Russia's nuclear energy agency, said: "The point of the agreement we will sign today is to create a legal base for co-operation.
"We will sign an agreement on co-operation in the nuclear sector which includes the building of a power plant, of a scientific reactor, training, co-operation in nuclear safety and exploration of uranium."
Gazprom, the Russian gas giant, and Nigerian National Petroleum Corporation are also slated to sign a gas agreement during the visit.
The Russian company wants a stake in Nigeria's vast gas deposits and is said to be ready to invest in energy infrastructure to obtain access.
One major project it wants to become involved in is the Trans-Saharan Gas pipeline, a project aimed at sending Nigerian gas to Europe, and supported by the European Union as a way to diversify its energy resources.
Gazprom has complained it is far behind its foreign competitors in Africa, saying it is ready to mount a challenge to companies like Royal Dutch Shell, Chevron and ExxonMobil who are investing in the continent.
Alexei Vasilyev, who is travelling with Medvedev and is head of the Africa Institute at the Russian Academy of Sciences, said: "They [Gazprom] are planning to cover all of Nigeria with pipelines. There is an acute need for energy in the country.
"Africa's oil and gas reserves are rising fast. That's the region with which we have to co-operate if we position ourselves as a great energy power."
A Kremlin official said: "With a view to Nigeria's membership in Opec and the Gas Exporting Countries forum, the presidents will discuss the issue of ensuring global energy security, as well as international co-operation in overcoming the world financial and economic crisis."
The two sides will also sign an agreement on co-operation in space and on mutual protection of investments.
Moscow's ties with many of its former client states came to a sudden halt with the collapse of the Soviet Union but the Kremlin has now emphasised its wish to revive relationships in Africa.
The continent is rich in oil, gas, diamonds, metals and uranium and Russia hopes to catch up with China, which has already invested millions of dollars there, in the race to exploit its resources.
Nigeria is Russia's second largest trading partner in sub-Saharan Africa, after South Africa, but at just $300m last year, the amount of trade between the two countries is still relatively insignificant.
Vladimir Putin, Medvedev's predecessor, became the first ever Russian president to travel to sub-Saharan Africa when he visited South Africa and Morocco in 2006.