Pogba beat out team-mates Zlatan Ibrahimovic and Henrikh Mkhitaryan for the inaugural honour, which was awarded after Friday's Europa League draw in Monaco.
Frenchman Pogba scored three goals, including the opener in the 2-0 final win over Ajax, and started all 15 games in United's championship run.
"I'm really honoured to be the first to win the best player for the UEFA Europa League," Pogba, who did not attend the ceremony as he prepares for Saturday's Premier League match against Leicester, said on United's website.
"Hopefully this season will be as good as last season - let's see!"
United's victory earned them an automatic place in this season's Champions League, where they were drawn in a group with Benfica, Basel and CSKA Moscow on Thursday.