"An agreement on cooperation for the peaceful use of nuclear energy to meet the growing power demand in the country was signed between the two countries in Moscow on Friday," a foreign ministry spokesman told Reuters.
Bangladesh Foreign Minister Dipu Moni and her Russian counterpart Sergey Lavrov witnessed the signing of the agreement between Russia's atomic energy corporation Rosatom and the Bangladesh Atomic Energy Commission (AEC).
Bangladesh had requested the Russian authorities to assist in establishing two nuclear reactors with a capacity of 1,000 megawatts each by 2015, the spokesman said.
The plants are expected to cost up to $2 billion and to begin generating electricity by 2014, officials of the ministry of power, energy and mineral resources said.
Bangladesh has plans to set up the nuclear power plants at Rooppur, 200 km (125 miles) northwest of the capital Dhaka, to help deal with growing power shortages.
Growing concern over power shortages led Bangladesh to consider nuclear energy as natural gas reserves are fast depleting and most coalfields remain unexploited.
Bangladesh now has nearly 60 power plants, mostly decades old and all fueled by gas or coal.
A power official said the country of 150 million experiences daily power shortfalls of 2,000 megawatts. Peak-hour demand stands at about 5,500 megawatts.
According to the agreement Rosatom will help Bangladesh AEC in designing, construction and operation of nuclear power and research reactors.
It will also supply nuclear fuel, take back spent nuclear fuel, manage nuclear waste, and train personnel for operation and maintenance of the plant.