The 25-year-old has scored 39 goals for the Bhoys this season, the latest of which came on Saturday in a 3-1 victory over Hearts that effectively wrapped up a fifth straight title for the club.
Griffiths fought off competition from Dundee duo Kane Hemmings and Greg Stewart in addition to Aberdeen's Jonny Hayes to add the award to the FWA Player of the Year and PFA Young Player of the Year gongs he won in 2013.
He becomes the third Celtic player in a row to win the award, and teammate Kieran Tierney was also honoured at the ceremony by winning the young player's prize.
Rangers boss Mark Warburton was named the manager of the year in his maiden campaign having steered the Ibrox outfit to the Scottish Challenge Cup, the Scottish Championship title and the Scottish Cup final.
That success also helped to earn Rangers skipper Lee Wallace the Scottish Championship Player of the Year award.