The 22-year-old Arsenal target saw off competition from team-mate Callum McGregor, Rangers forward Alfredo Morelos and Dundee United striker Lawrence Shankland.
The Frenchman netted 28 goals for Celtic last season including 22 in 27 league matches.
Edouard has been linked with several Premier League clubs but has hinted he will still be at Celtic next term.
“Every season we want to win the title. This year is nine-in-a-row, and next year I hope it is 10 in-a-row. This will be historic for the club.
“It’s very important for the club, for the fans, for the team, for all of the staff. We now need to go back to work for next season, and I hope that we can win this title for 10 in-a-row.”
It is the seventh straight year that a Celtic player has won the award and Edouard follows Kris Commons, Craig Gordon, Leigh Griffiths, Scott Sinclair, James Forrest and Scott Brown in claiming the prize.
Griffiths took the trophy on the previous occasion the award did not end up at Celtic Park, winning it in 2013 while playing for Hibernian.