Kante has signed a five-year contract at the west London club and is now officially a Chelsea player.
"I am so happy to have signed for one of the biggest clubs in Europe. It's a dream come true for me," he said on Chelsea's club website.
"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 one year ago for just £5.6m, winning the title in his first season at the Foxes.
N'Golo Kante may not be the only Leicester player to leave this summer as attacking midfielder Riyad Mahrez is also allegedly seeking a new club.