In a statement, it said "the construction of this nuclear power plant in Burkina Faso is intended to cover the energy needs of the population."
The West African nation has been ruled by a military junta since last year and has sought to diversify its international partners, moving closer to Moscow in particular.
The agreement was signed at the Russian Energy Week event in Moscow, by Burkina Faso's energy minister, Simon-Pierre Boussim, and Nikolay Spassky, the deputy director general of Russia's state atomic energy agency Rosatom.
The document "fulfils the wish of the president of (Burkina) Faso, Captain Ibrahim Traore, expressed last July at the Russia-Africa summit during a meeting with his Russian counterpart Vladimir Putin," the statement added.
Rosatom said in a statement that "the memorandum is the first document in the field of the peaceful use of atomic energy between Russia and Burkina Faso."
It said the agreement laid the foundations for cooperation in areas including the use of nuclear energy in industry, agriculture and medicine.
Just under 23 percent of Burkina Faso's population had access to electricity at the end of 2020, according to the African Development Bank.
"We plan, if we can, to build nuclear power plants by 2030, in order to solve the problem of the energy deficit," Russia's TASS news agency quoted Boussim as saying on Thursday.
"Our challenge is to double our electricity production by 2030, which will allow us to boost the industrialization of Africa," he added.
Burkina Faso imports a large part of its electricity from neighboring Ivory Coast and Ghana, while producing some electricity locally — mainly through hydroelectric or solar power.
The only nuclear power plant on the African continent is near Cape Town in South Africa.
Burkina Faso has distanced itself from France, its historic partner and former colonial ruler.
At a Saint Petersburg summit in July, Russian President Vladimir Putin announced that Moscow would deliver free grain to six African countries, including Burkina Faso, over the coming months.
In early September, a Russian delegation visited Ouagadougou to discuss developing military cooperation with the ruling junta.
Burkina Faso has faced years of deadly militant violence, which has left more than 17,000 civilians and troops dead and over two million people displaced.