Musa, who was linked with a move to the Barclays Premier League champions in January, is set to fly to England for a medical on Wednesday.
According to Russian media, the fee will be £16.6million, making the 23-year-old Leicester's new club-record signing, just days after French midfielder Nampalys Mendy arrived at the King Power Stadium for a new club-high fee of £13million.
"Everything has been finalised and Musa will be in England for his medical on Wednesday," Musa's agent Tony Harris told BBC Sport.
Musa, who can play as a winger or a striker, joined CSKA in 2012 and has scored 54 goals in 168 games for the Russian club
The 2015-16 season was his most prolific with 13 goals in 29 Russian Premier League matches.
He made his international debut against Madagascar in September 2010 and has scored 11 times in 58 appearances for his country, including two goals in Nigeria's 3-2 defeat to Argentina at the 2014 World Cup in Brazil
Source: PA