The Italian has been unemployed since resigning from his position as England manager in February and had been heavily linked with the Russia job after being included on their initial shortlist.
"If everything is completed in the best possible way, as the announcement from the Russian Football Union states, I will be happy and proud," Capello told 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."
Nikita Simonyan, Vice-President of the Russia FA, said: “We have decided to appoint Fabio Capello as the new coach of the national side. We’ll wait for the arrival of Capello in the next few days so we can iron out the last few details and he can then sign his contract.”
Capello replaces Dick Advocaat, who was at the helm during the Russians’ disappointing UEFA EURO 2012 campaign – where they were eliminated at the group stage – before leaving to take charge of PSV Eindhoven.
World Cup ambitions
Russia failed to qualify for the 2010 FIFA World Cup after losing a play-off against Slovenia under former coach Guus Hiddink, and have been drawn in Group F of European qualifying for Brazil 2014.
They share the group with Portugal, Israel, Northern Ireland, Azerbaijan and Luxembourg. Capello’s first competitive games will be a double-header, hosting Northern Ireland on 7 September before travelling to Israel four days later.
The 66-year-old led England at South Africa 2010, but the Three Lions were thrashed 4-1 by Germany in the Round of 16 after narrowly progressing from a section containing USA, Algeria and Slovenia.
Capello has a wealth of experience, however, having previously coached AC Milan, Juventus, Real Madrid and Roma, winning five Serie A titles, La Liga twice and a UEFA Champions League along the way.
His reign is likely to begin with a friendly against Côte d'Ivoire in Moscow on 15 August before the quest to bring Russia to another appearance at a FIFA World Cup starts, ahead of hosting the event in 2018.