Slutsky replaces Fabio Capello, who departed last month after poor results in the European Qualifiers left Russia sitting third in Group G, outside the automatic qualifying places.
Slutsky’s contract runs only until the end of the qualifying campaign in October for group games, or November for the play-offs.
Russia’s first home-grown coach for nine years, Slutsky, won the Russian Premier League title with CSKA in 2013 and 2014.
“The leadership of Russian football came to our club with a request to let me head up the national team,” Slutsky said on the CSKA website.
“Taking into account the difficult situation the national team has ended up in, I couldn’t refuse the offer. To manage your country’s team is a great honor and responsibility.”