Maddison, who is coming off the back of an excellent season in the Championship, has signed a five-year contract the Foxes that will run until 2023.
"We talked about the type of player I am, how I'm going to fit into his style of play and everything sounded really promising. I haven't looked back since that phone call.
"Leicester just seems like the right fit for me. I've got a good feel about the Club and I can't ignore that, in my head and my heart. I felt like this was the right place for me to be, so I'm delighted and can't wait to get started."
Leicester have already secured summer deals for Jonny Evans and Ricardo Pereira since the end of 2017/18 and Maddison's arrival will take their spending close to £50m. Georgian centre-back Solomon Kvirkvelia is also closing on a move from Lokomotiv Moscow.