Ahmed Musa scored 54 goals in 168 games for CSKA Moscow
Musa, 23, joins the Premier League champions after helping CSKA win the Russian title.
Southampton, Everton and West Ham were interested in the forward.
Musa is Leicester’s fourth signing of the summer after goalkeeper Ron-Robert Zieler, defender Luis Hernandez and midfielder Nampalys Mendy.
Leicester’s new signing joined CSKA in 2012 and scored 54 goals in 168 games, and has scored 11 times in 58 appearances for Nigeria since making his debut in 2010.
His first goal in that Group F game was his country’s fastest at the tournament, coming after just four minutes.