The France midfielder has turned his back on the Premier League champions to move to Stamford Bridge in a deal thought to be worth around £32million.
Kante, who has signed a five-year contract with the Blues, was an integral part of Leicester's shock title success last year.
But rather than stay and attempt to defend their crown, as well as play in the Champions League, the 25-year-old has opted to link up with new Chelsea boss Antonio Conte.
He told the club's official website: "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."
Kante, signed for Leicester last summer from Caen for £5.6million, was a revelation during his maiden season in England.