"Though Capello has not signed a contract yet, a principal agreement with the Italian had been reached and de-facto he has become Russia coach," the RFU said in a short statement on its website (www.rfs.ru).
Acting RFU chief Nikita Simonyan said the 66-year-old Italian would arrive in Moscow on Friday.
"He is coming tomorrow afternoon and on Saturday he'll watch the (Russian Premier League) match involving CSKA Moscow," Simonyan told local media. "Then the following day, he's going to St Petersburg to watch (Russian champions) Zenit."
Capello, who has had success coaching top clubs such as Real Madrid, AC Milan, AS Roma and Juventus and quit as England boss in February, replaces Dutchman Dick Advocaat, whose tenure ended with Russia's group stage exit from Euro 2012.
Advocaat had announced before the tournament that he would return home to take charge of PSV Eindhoven.
Capello, who becomes Russia's third successive foreign coach, will be tasked with blooding new players into an ageing team, something his predecessor failed to do in his two years at the helm.
Russian media reported Capello would earn up to 10 million euros a year after signing a contract through to the 2014 World Cup, with the possibility of extending it for another two years.