The ITAR-Tass news agency quoted Russian football federation head Nikita Simonyan as saying the decision to appoint Capello was made Monday.
Simonyan said all that is needed is a "final agreement on terms of the agreement."
"If everything finishes in the best of ways, as the Russian Federation has announced, I will be happy and proud," Capello told Italian news agency ANSA. "I am happy. If, as I believe, everything goes well with sorting out the contract details, it will be a splendid adventure. Russia is a great country."
Capello emerged last week as the clear favorite among 13 candidates to replace Dick Advocaat, who resigned after Russia failed to make it beyond the group stage of the European Championship.
Capello, who stepped down as England coach in February, has previously managed Real Madrid and Inter Milan.