The 52-year-old has signed a contract until August 1, 2018, Russian Football Union President Vitaly Mutko said.
"There were four candidates to choose from for the position of head coach: Cherchesov, Kurban Berdyev, Sergei Semak and Alexander Borodyuk," Mutko told reporters.
"We spoke with all of them. We came to the decision that Cherchesov fits the criteria best of all."
Former Russia manager Leonid Slutskiy resigned after the team's disappointing campaign at the Euro 2016 where they finished bottom of group B and failed to qualify for the knockout stages.
Cherchesov's first match in charge of Russia will be a friendly against Turkey on Aug. 31 in Antalya. Being the hosts, they would not need to qualify for the 2018 World Cup.
"At the executive committee meeting, I said that I had always played in teams where there were high expectations," Cherchesov said. "However, it would be frivolous to set ourselves the goal of winning the 2018 World Cup.
"The task at the moment is to create a competitive environment within the team and to give the players the opportunity to show their capabilities as well as trying to assess them and their opponents.
"There is no point in making any loud statements at the moment."
Cherchesov has coached a number of clubs in his home country, including Spartak Moscow and Dynamo Moscow. He took over as manager of Legia Warsaw in October, 2015 and helped the club win the Polish league and the Cup.
(Reporting by Dmitriy Rogovitskiy; editing by Sudipto Ganguly)
