The England international joined the Blues on deadline day in a £35m deal.
Kante is now reunited with his former Leicester team-mate, with both players quitting the Foxes following their Premier League title triumph.
And Chelsea star Kante has hailed Drinkwater, claiming he’s desperate to win more trophies with his new midfield partner.
“I am pleased for him to come into Chelsea,” Kante told Starsport.
“We need everyone, especially after our time together in Leicester. I hope it could be something like Leicester or even more, I hope.
“We did a special year together in Leicester to win the league.
“It wasn’t expected and I really enjoyed the season that I spent with him and I am happy that he chose to join Chelsea and I am happy to play with him again.”
Drinkwater is yet to feature for Chelsea under Antonio Conte this season.
Kante, Cesc Fabregas and Tiemoue Bakayoko have been the Italian’s preferred midfield trio.
Chelsea are back in action this weekend when the Blues face Arsenal at Stamford Bridge on Sunday.
The Blues have impressed this season, winning three of their opening four league games.
