The RFU's executive committee approved the deal at a meeting to discuss the World Cup which ended on July 15, the Interfax news agency reported, citing the union's acting president Alexander Alayev.
The contract will likely be signed on Friday and could be extended for another two years when it expires, lawmaker Igor Lebedev, a member of the RFU's executive committee was quoted as saying by Interfax.
Under Cherchesov, the hosts defied expectations by reaching the quarter-finals despite being the lowest ranked team in the tournament.
They followed up group stage victories over Saudi Arabia and Egypt by knocking out 2010 World Cup champions Spain in the last 16. Russia's run was halted in the quarter-finals when they were beaten on penalties by eventual finalists Croatia.
It was Russia's best World Cup run since the break-up of the Soviet Union.
(Writing by Tom Balmforth, editing by Pritha Sarkar)
