The 23-year-old is to join the Premier League champions for a club-record fee of £16.6m, according to the player’s agent.
Leicester have been chasing the Nigerian international’s signature since May, when boss Claudio Ranieri first contacted the Russian outfit with regards to Musa’s availability.
A deal is now close to being completed, with agent Tony Harris telling BBC Sport: “Everything has been finalized and Musa will be in England for his medical on Wednesday.”
CSKA coach Leonid Slutsky added: “He’ll be leaving on Tuesday. And if you look at the way things are done over there you’ll see he is a player just made for English football.”
Musa, who can play as a wide player or up top, has previously been linked with a move to Southampton, Everton and West Ham United.