Kante, 25, is new manager Antonio Conte's second acquisition, following Olympique Marseille's Belgium striker Michy Batshuayi, and arrives after playing at Euro 2016.
"I am so happy to have signed for one of the biggest clubs in Europe. It’s a dream come true for me," Kante told www.chelseafc.com.
"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."
The clubs did not disclose financial details but British media put the fee at 32 million pounds ($42.20 million).
Kante was Claudio Ranieri's first signing at Leicester, joining for six million pounds after two seasons at Caen.
He had a successful season last term, helping the 5,000-1 outsiders win the title for the first time before joining up with France.
Kante played in the opening match but was banned for the quarter-final, came on in the semi and was an unused substitute in the final which the hosts lost 1-0 to Portugal after extra time.
SPECIAL SEASON
Kante played in all but one of Leicester's league games and made most overall tackles and interceptions in the competition.
His efforts saw him named in the PFA Team of the Year.
"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," said Kante.
His campaign contrasted with Chelsea's dismal season as they finished a lowly 10th and failed to qualify for Europe.
Technical director Michael Emenalo said: "N’Golo is a fantastic signing. 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."
Born in Paris, Kante played for amateur side Suresnes until he was 19 when he moved north to join Boulogne. He was spotted by second-tier Caen and moved to the Normandy club and helped them earn promotion to Ligue 1 in his first season.
($1 = 0.7583 pounds)
(Editing by Tony Jimenez)
