Chelsea paid Leicester £35m for the midfielder, who joins Kante at Stamford Bridge.
The pair enjoyed great success together under Claudio Ranieri in Leicester’s title winning season.
“I played with N’Golo for a season and there was not really a game I didn’t enjoy playing next to him,” Drinkwater told Chelsea‘s official website.
“I am looking forward hopefully to carrying on where we left off.
“I think we hit it off from the first game and after that we did not really lose.
“He is a top lad, the most down-to-earth person you will meet.
“I can’t see him changing much and I am looking forward to meeting him again.”