Maddison played a starring role for Norwich in the 2017-2018 EFL Championship season, his performances earning a spot in the Professional Footballers' Association's (PFA) Team of the Year for England's second tier.
He scored 15 goals and set up another eight, with his promising early season form earning him a debut for England's Under-21 side when they faced Ukraine in November.
Norwich's poor financial position meant a sale was inevitable, but they have been praised for managing to secure a club-record sale fee for the 21-year-old, who had only made three first-team appearances for the club before the season which just finished.
Maddison becomes Leicester's third signing ahead of the new campaign, following on from Ricardo Pereira and Jonny Evans.
The midfielder has signed a five-year deal at the King Power Stadium.