The France international has been persistently linked with a move away from the Wanda Metropolitano, 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 the 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 their momentum checked by Griezmann’s opener, and an injury to captain Dimitri Payet before the break came as a further blow to their hopes.
Their 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 victory with only one minute remaining.
Atleti’s win secures a third Europa League triumph, pulling them level with Juventus, Inter and Liverpool behind five-time winners Sevilla on the competition’s roll of honour.