The 26-year-old, who picked up 34 league appearances in his debut season with the Blues, was presented Football Writers' Association Footballer of the Year award.
"It's special because I couldn't even say I'm the best player but it's very special and a great honour," Kante said at the ceremony.
"It's not only me. I owe so much to my team-mates because we have achieved so much together this season and we still have the FA Cup.
"It is very special, a few years ago I was playing in the French lower divisions. Five years ago I wasn't even professional so to receive this kind of award means I am the kind of player I cannot even imagine being here."