“We have decided to name Fabio Capello as the new manager of our national team," RFU acting president Nikita Simonyan told local media.
"We await Capello in Moscow over the next few days for the final details and the signing of the contract."
The 66-year-old Italian, who quit as England boss in February, said he was happy to work in Russia.
"I am happy, if contract negotiations go well as I believe they will, it will be a wonderful adventure, as Russia is a great country," he told Italian news agency ANSA.
Capello will succeed Dutchman Dick Advocaat, whose contract expired following Russia's failure to get past the group phase at Euro 2012. He will become Russia's third foreign coach in a row after Advocaat and his compatriot Guus Hiddink.
Capello was regarded as favourite for the job  after coming to Moscow last Thursday for talks with Simonyan and Sports Minister Vitaly Mutko.
Russian media reported the Italian is set to sign a two-year contract, with the possibility of extending it for another two years, with an annual salary of 10 million euros.