The Italian held successful talks with the Russian Football Union (RFU), who have confirmed he is the man they believe can guide the team to World Cup qualification in 2014.
"Today we have decided to name Fabio Capello as the manager of Russia," RFU vice-president Nikita Simonyan told the Itar-Tass agency.
"We are now waiting in Moscow for the finalisation of the remaining details of the contract before he signs.
"Once (Capello) and his representatives arrive, we believe they will sign the contract. I think it will happen on Wednesday or Thursday."
Capello has been out of work since leaving the England job in February in protest at the Football Association stripping John Terry of the captaincy after he was charged with making a racist remark to Anton Ferdinand. Terry was acquitted of the charge at Westminster magistrates court on Friday.
In Russia, he succeeds Dick Advocaat who left to take up the coach's role at PSV Eindhoven following the team's group-stage exit at Euro 2012.
Reports have suggested 66-year-old Capello has been offered a six-year deal which will take him up to the 2018 World Cup which Russia are hosting.
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 - and two Primera Division championships. He also won the Champions League with AC Milan in 1994.
Capello is relishing the challenge of guiding Russia.
"If everything is completed in the best possible way, as the announcement from the Russian Federation states, I will be happy and proud," Capello told Italian news agency ANSA.
"If, as I believe the case will be, all goes as planned in terms of the contract, it will be a splendid adventure.
"Russia are a great nation."