There had been much speculation the former England boss was among the favourites for the vacant job and a Russian Football Union spokesman confirmed to Press Association Sport that he has signed a two-year deal.
The Italian succeeds Dick Advocaat, who took charge of Eredivisie outfit PSV Eindhoven after Russia were eliminated in the group stages of Euro 2012.
Capello, who resigned as England manager in February, was earlier this month on a shortlist of 13 candidates for the job, with Harry Redknapp and former Barcelona boss Pep Guardiola also mentioned by the RFU.
But speculation has grown since that the 66-year-old was their man and he is now set to complete the formalities, with a press conference scheduled for Thursday afternoon.
The RFU will hope Capello will prosper after Russia started promisingly at the European Championship, by beating Czech Republic 4-1, before being eliminated after a draw with co-hosts Poland and a defeat to Greece.
Similarly, Capello will be looking to rebuild his reputation after a less than impressive four years with England.
After taking charge in 2008, he was initially a great success after England comfortably qualified for the 2010 World Cup but matters soon went awry after a disappointing tournament that ended with a crushing 4-1 defeat by rivals Germany in the second round.
The former AC Milan, Roma and Real Madrid boss guided England into this year's tournament in Poland and Ukraine but quit his post in acrimonious circumstances after the Football Association stripped John Terry of the captaincy due to the Chelsea defender being charged with making a racist remark to Anton Ferdinand. Terry was subsequently cleared in a magistrates court trial.
Prior to his mixed stint with England, Capello was widely viewed as one of the best coaches in the world.
His record includes seven Serie A titles - although two of these were later revoked after Juventus were implicated in the Calciopoli match-fixing scandal - and two Primera Division championships. He also won the Champions League with AC Milan in 1994.