The defensive midfielder joined from Caen last summer for £6m and went on to make 40 appearances in Leicester's Premier League-winning campaign.
Kante, 25, was part of the France squad that reached the final of 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," he said.
Kante is Chelsea's second signing of the summer after Belgian striker Michy Batshuayi joined from Marseille.
"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," said Kante.
Leicester said they accepted a club record fee on Friday before Kante finalised terms and completed a medical.
"Despite the offer of a substantially improved, long-term contract, it became apparent that N'Golo's wish was to join Chelsea," said a Foxes statement.
Leicester striker Jamie Vardy turned down a move to Arsenal earlier in the summer, but there is continued speculation winger Riyad Mahrez could leave.
Chelsea technical director Michael Emenalo described Kante as a "fantastic" signing with "exceptional quality".
"He is a perfect fit in terms of Antonio Conte's philosophies and the style of football he wants to play," added Emenalo.
Meanwhile, Conte lost his first game in charge as they were beaten 2-0 by Rapid Vienna in a friendly. Chelsea fielded a strong side captained by John Terry and including Branislav Ivanovic, Nemanja Matic, Willian, Ruben Loftus-Cheek and Diego Costa.
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His firm, Cameron Pace Group and its Chinese partners will develop advanced equipment for 3D filming.
The move comes amid a boom in China's movie industry and a growing demand for 3D films in the country.
Various Hollywood filmmakers have been trying to tap into the Chinese market.
"The future of entertainment is 3D and we believe that the future of 3D is right here in China," Mr Cameron was quoted as saying by the Associated Press news agency.
Earlier this year, Chinese authorities had announced that they will allow an additional 14 foreign films to be shown in the country, if the movies are made in 3D or for the big-screen Imax format.
China's movie industry has seen robust growth in the past few years.
Ticket sales in the world's second-largest economy surged 29% to 13.1bn yuan ($2.1bn; Â£1.3bn) in 2011. They are forecast to rise further, by around 20% in the current year.
The growth in its market has seen various Hollywood filmmakers and studios announcing joint ventures with Chinese firms.
Earlier this week, Dreamworks Animation announced plans to co-produce the next Kung Fu Panda movie with its Chinese partners. The firm said it was also planning to open an entertainment district in the country.
In April, Walt Disney Company, the world's largest entertainment firm, said that it plans to co-produce Iron Man 3 with Beijing-based DMG Entertainment.
Mr Cameron said that the robust growth in the country's market made it attractive destination.
"This is the best place for us to create a kind of a second home," he said.

Contact has been made between the two clubs, although there is no agreement over a deal yet.
The France player, who signed for United for £25m in July 2015, would be reunited with former Southampton manager Ronald Koeman at Goodison Park.
Red Devils boss Jose Mourinho will sanction any deal for the 27-year-old, who is not part of his long-term plans.
Schneiderlin has played 11 minutes of Premier League football this season and he has not been included in the United squad for Wednesday night's league match at Crystal Palace.
Koeman was keen to keep the Frenchman at Southampton during his time as manager in 2014, and the Dutchman views him as a key component in his plans to strengthen Everton's midfield.
It is also understood Koeman is keen on United and Netherlands forward Memphis Depay.
The Dutchman has also attracted interest from Germany and Italy, with Roma among the clubs keen on the 22-year-old, who joined United from PSV Eindhoven for £31m last year.
Chelsea have signed Leicester City midfielder N'Golo Kante on a five-year deal for a fee believed to be in the region of £30m.
[NEXT_CONCEPT]
James Cameron, the creator of the blockbuster film Avatar, has announced a joint venture with two Chinese firms in a bid to capture the country's fast-growing movie market.
[NEXT_CONCEPT]
Everton are interested in signing Manchester United midfielder Morgan Schneiderlin.