The Denmark goalkeeper spent more than a decade at Leicester after arriving from Leeds United, winning a Premier League title, an FA Cup and a Community Shield during his time at the King Power Stadium.
Schmeichel made 479 appearances in all for the Foxes, featuring in more Premier League games for Leicester than any other player (276), and, barring injury, will be a part of the Denmark squad for the World Cup in Qatar later this year.
Speaking to Leicester's official website on the announcement of Schmeichel's departure, Chairman Aiyawatt Srivaddhanaprabha said: "Throughout his time with us and particularly as a captain and vice-captain, Kasper has always been a player willing to stand up and take responsibility, leading the team with distinction.
"His influence and his leadership on and off the pitch speak volumes about him as a professional, as a football player and as a human being.
"I know Leicester City supporters share the respect we all have for a player of Kasper's standing after all his accomplishments as a footballer and captain and will join me in wishing him the very best for the next stage of his career in France with OGC Nice.
"It's clear to everyone who has watched him perform that Kasper has given everything to Leicester City every time he has played and the experiences shared between him, the club and our supporters over the last 11 years mean he will always remain a part of this family."
Schmeichel sits behind only West Ham's Lukasz Fabianski (284) and Manchester United's David de Gea (283) for appearances in the Premier League since the start of the 2014-15 season.
Nice also announced the signing of young centre-back Mattia Viti from Empoli earlier on Thursday (AEST), adding to other new arrivals in the transfer window Aaron Ramsey, Alexis Beka Beka, Rares Ilie and Badredine Bouanani.