Earlier this month, it was claimed that Southampton had agreed a fee for the playmaker, only for Leicester to quickly match the Saints' bid and emerge as favourites to sign the young Englishman.
Negotiations quickly progressed to an advanced stage, and the Foxes are now in a position to announce the acquisition of the 21-year-old on a five-year contract.
Maddison told the club's official website: "I'm delighted. I'm really happy to be here. I had a good chat with the manager about football and how he wants me to play, how he likes to play and I was sold. 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."
Maddison contributed 14 goals and eight assists in 44 Championship appearances last season.