The 23-year-old is expected to stay at the King Power Stadium for four years, until 2020, after passing a medical on Friday.
According to Daily Mail, the fee is believed to be around £18 million with the forward hoping to link up with his new teammates on the club’s pre-season training camp in Austria next week.
The Foxes are expected to announce the capture of the Nigerian, later on Friday.
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Musa scored 13 goals and provided five assists for CSKA in 30 Russian Premier League games last season. He has also scored 11 goals in 58 appearances for Nigeria.