The Central Asian country is the world's largest producer of uranium and has massive oil reserves but it suffers from chronic energy shortages.
The "Yes" vote won 71.12 percent in Sunday's referendum and the turnout was 63.66 percent, the Kazakh electoral commission said Monday.
China, France, Russia and South Korea are in the running to build the new power station, which is to be located on the shores of Lake Balkhash.
President Kassym-Jomart Tokayev, who was elected in 2019, says the plant would be "the biggest project in the history of independent Kazakhstan".
Tokayev indicated Sunday that he preferred an "international consortium made up of global companies equipped with cutting-edge technologies".
The "Yes" camp has dominated throughout the campaign and opponents concerned about potential accidents struggled to make themselves heard.
Dozens were arrested in the weeks preceding the referendum, according to local private media.
The issue of nuclear power is sensitive given that between 1949 and 1989, the Soviet Union carried out around 450 nuclear tests there, exposing 1.5 million people to radiation.
The power station is due to be built near the semi-abandoned village of Ulken in the Kazakh steppes on the shores of Lake Balkhash, Central Asia's second-largest lake.
To bolster turnout, the authorities cleared Kazakhs to vote even if they were not registered on the electoral lists. Buses were free in large cities on referendum day to facilitate access to polling stations.
"The referendum itself is further proof of the enormous changes that have occurred in Kazakhstan over the past five years, a new clear manifestation of the concept of a listening state," Tokayev said before the vote.
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