It said the project would "deepen and broaden the beneficial economic and scientific ties between the two countries, taking into consideration the fact that both are members of the IAEA and parties to the agreement on non-proliferation".
The centre is to have a 10-megawatt light-water research reactor, as well as facilities for processing and storing radioactive waste, Rosatom said.
Supporter and supplier
Russia, along with China, has become a major supporter and supplier of arms to Myanmar since the West imposed sanctions in 1988 accusing its military government of repressive and undemocratic practices.
The two countries last year vetoed a US-drafted UN Security Council resolution urging Myanmar to stop persecuting political prisoners.
Russia is already building a nuclear power station in Iran, suspected by the US of seeking to develop nuclear weapons.
According to a 2004 research paper by the Australian National University, Myanmar, formerly known as Burma, asked Russia in 2000 for help in starting a civilian nuclear programme.
Moscow backed out in 2003, apparently because they could not agree on payment details.
Earlier this month a report from US-based democracy watchdog organization Freedom House labelled Myanmar as having one of the worst records on human rights in the world.
The military has run Myanmar since 1962, ignoring a 1990 landslide election victory by Aung San Suu Kyi, the detained leader of the opposition National League for Democracy.
Awarded the 1991 Nobel Peace Prize, she has been in prison or under house arrest for 11 of the past 17 years.