The France international has been persistently linked with a move away from the Spanish capital, with Barcelona reported to be among his biggest admirers.
But if this season is to be his last with the club, Griezmann produced the perfect parting gift at Groupama Stadium.
A Marseille error opened the door for the forward to put Atleti in front after 21 minutes, before a delightful finish doubled the advantage for Diego Simeone's men early in the second half.
The Ligue 1 outfit had started brightly but had its momentum checked by Griezmann's opener, and an injury to captain Dimitri Payet before the break came as a further blow to its chances.
Its best chance to pull a goal back came 10 minutes from time, when substitute Kostas Mitroglou headed against the post, but Gabi wrapped up the win with a late third.
Atleti held firm for a third UEFA Europa League triumph, pulling it level with Juventus, Inter Milan and Liverpool behind five-time winner Sevilla on the competition's roll of honour.