Monga made his Premier League debut for the Foxes at the age of 15 and has decided to join City despite interest from other top clubs.
The 17-year-old played 37 times for Leicester and was also the youngest player to start a game for the club.
Jeremy Monga (right) in action for Leicester against West Bromwich Albion (Nick Potts/PA).Monga told City’s website: “When I became aware that Manchester City were interested, I knew instantly this was the right choice for me.
“For any young footballer, to become part of this amazing club is a dream come true.”