Drinkwater, who has yet to make his Chelsea debut due to a calf problem, played alongside Kante in midfield when Leicester finished top in 2016.
The partnership was broken when Kante moved to Stamford Bridge for £32million last year, but now Drinkwater has joined him in west London for £35m.
Speaking for the first time about Drinkwater’s acquisition, Kante said following Tuesday night’s 6-0 Champions League win against Qarabag: “I am pleased for him to come into Chelsea.
“We need everyone, especially after our time together in Leicester.
“I hope it could be something like Leicester or even more.
“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.
“I am happy that he chose to join Chelsea and I am happy to play with him again.”