The Frenchman completed his £30 million transfer on Saturday and was Conte's second signing after he arrived at the former English Premier League champions.
"At the beginning of the 2016-17 season, I chose to join Chelsea FC. It is a great club which has just recruited a great coach and want to reach high ambitions I share, Kante wrote on Twitter on Sunday.
"The club's project and the coach's speech have convinced me to join this new ambitious adventure."
The 25-year-old also thanked defending champions Leicester City and the fans for supporting him all through last season.
"This season I discovered the Premier League championship with FC Leicester," he wrote.
"I want to thank the leaders, my team-mates 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," he added.
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