Kante received the prize at the Landmark Hotel in London on Thursday in recognition of an outstanding season, in which the 26-year-old played an instrumental part in the Blues winning the title.
The France international fought off competition from his team-mate Eden Hazard and Tottenham forward Dele Alli, who were voted second and third respectively, after sealing his second consecutive Premier League crown.
Kante joined Chelsea last summer for £32million, having also played a key role in Leicester becoming champions 12 months ago.
"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.
"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."
Five Chelsea players were nominated by the 340 FWA members, with Hazard, David Luiz, Diego Costa and Cesar Azpilicueta also receiving votes.
But Kante collected more than 65 per cent of the journalists' votes, which were spread over a record number of 17 different players.
Graeme Souness praised the "fabulous" footballer and Pat Jennings said he would be welcome to extend his run of winning the Premier League with his own former team Tottenham.
Chelsea technical director Michael Emenalo joked he sent Leicester flowers after seeing Kante up close and believes there is even more to come.
"For those of you who don't know, I am the stand in for Antonio Conte who was supposed to give this speech," Emenalo said.
"Antonio decided not to do it because the Football Writers' Association couldn't find 25 awards for all of his players and he doesn't believe in individual awards.
"But if he was here, he would say about N'Golo that he is a fantastic player, very good in all tactical aspects, but he must improve.
"It is ridiculous to think that N'Golo Kante can improve, given the fact that he has improved two fantastic clubs and helped them win titles in the last couple of seasons."
Emenalo added: "I want to express the great pride that I personally have and the football club, and to be able to say that this wonderful player, this wonderful person is a part of our organisation.
"It gives me great joy tonight to say congratulations N'Golo and to wish you all the best, and hopefully continue to improve
From the Chelsea family, you're the pride and joy."
Source : PA
Source: PA