The Atletico Madrid star was rewarded for his outstanding performance in the 2017/18 Europa League.
The 27-year-old Griezmann won the award ahead of compatriot Dimitri Payet who led Marseille to the final only to lose to Atletico.
Griezmann's teammate Diego Godín who captained Atletico Madrid to the title was in third place.
The French star was named the winner in Monaco at the draw ceremony for the 2018/19 UEFA Europa League which his Atletico Madrid side will play no part in.
In the final against Marseille, Griezmann was awarded the match of the match as he scored the two goals that guaranteed Atletico Madrid's victory.
He also went on to have a fruitful outing at the and was awarded the silver ball.
Griezmann's Atletico Madrid side will face Borussia Dortmund, Monaco and Club Brugge in Group A of the 2018/19 UEFA Champions League group stage and the final of the tournament will be played in their home ground Metropolitano Stadium.