The Italian held successful talks with the Russian Football Union (RFU), with just the small matter of his contract left to confirm.
RFU vice-president Nikita Simonyan said: “Today we have decided to name Fabio Capello as the manager of Russia.
“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 added: “If everything is completed in the best possible way, as the announcement from the Russian Federation states, I will be happy and proud.
“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.”
Capello has been out of work since leaving the England job in February in protest at the FA’s decision to strip 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.