He takes over from Frenchman Raphael Saint-Andre, who had been in charge since May and oversaw eight matches including four wins and four defeats.
Russia missed out on a place at the 2015 World Cup, when they were beaten in a two-legged playoff by Uruguay in October.
Pervukhin has coached the Yenisey-STM club from Krasnoyarsk for several years, helping them to six national titles.
He must now decide whether he will combine both roles, or concentrate solely on the national team.
(Reporting By Dmitriy Rogovitskiy; editing by Toby Davis)
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