The 25-year-old completed a move to Chelsea on Saturday in what was a club-record sale for Leicester with the fee thought to be worth around €38 million to the reigning champions.
Kante, who was part of the France squad which reached the final of Euro 2016 on home soil, had only moved to the King Power Stadium 12 months ago but enjoyed a stellar debut season in England - playing a major role in delivering the title to the Foxes.
But, as part of an Instagram post which also paid tribute to the victims of the Nice terror attack, Kante said words from new Blues boss Conte were enough for him to leave the title holders.
“At the beginning of the new season, I chose to join @chelseafc,” he wrote.
“It is a great club, which has just recruited a great coach and want to reach high ambitions I share. The club’s project and the coach’s speech have convinced me to join this new ambitious adventure.
“I am now waiting to see my new club and give everything for a successful summer... And season of course!!”
Kante is the first big-name player to depart Leicester since their unexpected title triumph, with top-goalscorer Jamie Vardy turning down the chance to join Arsenal and instead signing a new deal with Claudio Ranieri’s side.
But reports persist that winger Riyad Mahrez could also soon be on his way out having turned down his own fresh contract offer.
Kante became an instant hit with the Leicester fans and thanked them for their support during what turned out to be an unforgettable year for the former Caen midfielder - who also made his international debut while at Leicester.
“The 2015/2016 past season will remain as an important season for me,” he wrote.
“I want to thank the leaders, my teammates and Claudio Ranieri for this fantastic season that saw us winning the title of England. Their confidence and also the fans’ will forever remain in my memory. And I again thank you all.”
Conte’s first game in charge of Chelsea ended in a 2-0 pre-season friendly defeat against Rapid Vienna on Saturday.
A strong side, captained by John Terry, and including Branislav Ivanovic, Nemanja Matic, Willian, Ruben Loftus-Cheek and Diego Costa fell behind to Brazilian teenager Joelinton’s eighth-minute goal.
Tomi Correa added a second with eight minutes remaining while, for the Blues, Costa squandered a good chance and academy graduate Ola Aina hit a post.
Afterwards, Conte confirmed that forgotten winger Juan Cuadrado will return to the club, having spent last season on loan at Juventus.
“Juan Cuadrado is a Chelsea player,” Conte said. “He will come back very soon.
“He’s in our squad, I’m very happy to have him and train him.
“I wanted him when I was a coach at Juventus and he will come back very soon and train and play with us. Now, he’s a Chelsea player and he’ll stay with us.”
Conte also maintained he will help Eden Hazard become one of the world’s best players.
“It is important for us to get Hazard back to his best condition, technically, physically and mentally. I spoke with him and I am very happy to train a fantastic player like him.
“Chelsea have players with great talent, who can become top, top, top players.
“At the moment the world doesn’t think they’re at the same level as (Lionel) Messi or (Cristiano) Ronaldo or Neymar. But there are players that can reach this level, I’m sure.
“The players must believe that they can become top, top, top. It is important for the manager to take the best and try to improve them.”
Former Chelsea striker Demba Ba faces a lengthy spell on the sidelines after suffering a horror leg break playing for Chinese Super League side Shanghai Shenhua.
The 31-year-old, who left Stamford Bridge in 2014, sustained the injury in the clash with Shanghai SIPG where his left leg tangled with defender Sun Xiang and was left at a right angle.
Chelsea, for whom he scored 14 goals in 51 appearances, wished their former player a speedy recovery.
The Premier League club tweeted: “All at Chelsea FC send our best wishes to former striker @dembabafoot. Get well soon Demba.”