The Italian was named Manager of the Year for guiding the Blues to the top of the Premier League table ahead of an expected title win in his first season in England.
Kante won Player of the Year, having continued his stellar performances for Leicester City after a £32 million move to Stamford Bridge, and looks on course to claim back-to-back titles.
Conte has thrived since becoming Jose Mourinho's permanent replacement, overseeing just losses as Chelsea opened up a 10-point gap over their nearest rivals.
The Italian is looking to emulate compatriot Carlo Ancelotti by winning the league and FA Cup in his first season at Stamford Bridge, with a quarter-final date against Manchester United upcoming.
Kante, meanwhile, will be hoping to add to the Premier League winners' medal of last season with another this term, becoming the first key player since Eric Cantona to win consecutive championships for different clubs.
Elsewhere, Tottenham pair Hugo Lloris and Dele Alli were named Goalkeeper and Young Player of the Year, while Fulham's Tom Cairney was crowned EFL Player of the Year.
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