Vardy played a key role in City's fairytale league triumph, contributing 24 goals.
The England international beat off competition from Foxes teammates Wes Morgan, Riyad Mahrez, N'Golo Kante and Kasper Schmeichel for the award.
Tottenham trio Harry Kane, Dele Alli and Toby Alderweireld, West Ham star Dimitri Payet and Arsenal ace Mesut Ozil were also nominated for the prize.
The 29-year-old Vardy had already been named Footballer of the Year by the Football Writers' Association, while Mahrez earlier scooped the PFA Player of the Year accolade.