"I feel very happy joining Leicester, for me it's one of the best clubs... and they are like a family," Musa told City's website (www.lcfc.com) on Friday.
"I'm very excited. I look forward to seeing the fans in the new season and I will do my best to make them happy."
The 23-year-old scored 13 goals in 29 league appearances last season as CSKA won the Russian title.
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Musa becomes the fourth signing for Leicester in the close season, following the arrivals of midfielder Nampalys Mendy, goalkeeper Ron-Robert Zieler and defender Luis Hernandez.
Claudio Ranieri's men start the new league campaign with a trip to promoted Hull City on Aug. 13.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Tony Jimenez)
