The Sun says he will be officially announced as a Foxes player later today.
The ¬£24million capture of one of the hottest properties in the Championship is a major coup for the manager Claude Puel.
The 21-year-old, who scored 14 league goals and had eight assists last season for Norwich, was hotly pursued by Southampton over the weekend and Mark Hughes believed he had won the tussle for the talented young midfielder.
However Puel pushed hard for the signing he sees as crucial to the way he wants Leicester to play this season as the Frenchman sees Maddison's vision and ability to play early passes as the perfect springboard for Jamie Vardy.
The Foxes have agreed to pay Norwich ¬£21million up front for Maddison with a further ¬£3million in add-ons if he reaches his full potential.