The lake, located in the southeast, is the country’s second-largest.
China’s National Nuclear Corporation, France’s EDF and South Korea’s Hydro and Nuclear Power had all bid to build the plant.
In their announcement on Saturday, the Kazakh authorities said that the three companies would be included in the consortium led by Rosatom but did not provide any details.
Observers say the idea of the consortium is a way for authorities to maintain good relations with all the countries involved but is unlikely to come to fruition and Rosatom will end up building the plant by itself.
Kazakh President Kassym-Jomart Tokayev has sought to keep good relations both with former colonial power Russia and with China, which borders the country to the east and finances major infrastructure projects in the region.
Rosatom has proposed financing the project and work will now begin to thrash out the details, the statement said.
The announcement comes a few days before Chinese leader Xi Jinping is due to visit Kazakhstan for a “China-Central Asia” summit.
Kazakhstan had nuclear power plants when it was part of the Soviet Union, in addition to hosting Soviet nuclear weapons.
It was also the site for Soviet nuclear testing.
After the break-up of the USSR in 1991, the new country gave up its nuclear weapons, with other ex-Soviet states Belarus and Ukraine; it decommissioned its nuclear power plants in the following years.
- Agence France-Presse