Kante – who has won the PFA, FWA and Premier League Player of the Year awards for this season – was a firm favourite to collect the club's main honour.
However, Hazard, who blossomed in the Blues's 3-4-3 system, became the second player in the club's history to win the award three times.
Frenchman Kante picked up the Players Player of the Year award, which was presented prior to the award's ceremony.
Speaking after being presented the award by David Luiz and Kurt Zouma, Kante said: "Because we spend so long together, and we win together and we lose together, to be named by the other players is something special,' he said. 'I spent a very good season here.
"We were unlucky we did not win yesterday (against Arsenal in the FA Cup final) but it was a good season and hopefully next season we are going to be stronger."