Slutskiy announced he would not extend his contract after Russia were knocked out of the European Championship last week, finishing bottom of Group B with one point from three games.
"The RFU would like to thank Leonid Slutskiy, who helped Russia to qualify for the 2016 European Championships, for his professionalism and we wish him all the success in his coaching career," the RFU said in a statement on its website (www.rfs.ru).
"Information regarding the new coaching staff of the Russian team will be published on the RFU's official website as soon as there is any information," it added.
The 45-year-old, who is also CSKA Moscow coach, had been in charge of the national team since August 2015.
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(Reporting by Dmitriy Rogovitskiy, editing by Ed Osmond)
