The 25-year-old has signed a five-year deal and becomes Antonio Conte’s second signing of the summer after Michy Batshuayi.
Kante was a revelation for Premier League champions Leicester last season after joining for £5.6million from Caen last summer.
He was named in the PFA Team of the Year, and went on to impress for France at Euro 2016.
Leicester wanted to keep the Frenchman at the club and offered him an improved four-year contract before Euro 2016, but he declined the offer to move to Stamford Bridge on a deal worth around £120,000 a week.
After completing his move to Chelsea Kante said: “I am so happy to have signed for one of the biggest clubs in Europe. It’s a dream come true for me.
“The opportunity to work with Antonio Conte, a brilliant coach, and some of the best players in the world was simply too good to turn down.
“My first season in English football was very special and now I hope to go on to achieve even more during my time as a Chelsea player.
“I am looking forward to meeting up with my new team-mates and helping the club achieve a lot of success.”
Chelsea technical director Michael Emenalo added: “N’Golo is a fantastic signing ahead of the new season and we are delighted to have been able to bring such a talented player to the club.
“He is a perfect fit in terms of Antonio Conte’s philosophies and the style of football he wants to play.
“For a player of his age he has already built up a wealth of experience and his exceptional quality will without doubt be a great addition to the team.”