Atletico won the 2012 Europa League, 2013 Copa del Rey and 2014 La Liga title during coach Diego Simeone's first three seasons at the club, but also lost in the 2014 and 2016 Champions League finals against Real Madrid.
That position is now occupied by Lyon, but Marseille are just a point behind them and Monaco could yet drop from second spot, with the final round of matches in France to be played this weekend.
Griezmann struck in either half as Madrid captain Gabi rounded off victory with a late effort.
"Griezmann today confirmed what he has been doing year by year", Simeone said after the game.
"I chose to start Dimitri, one of our best players", he said, as quoted by Sky Sports. Now we are in the UEFA Super Cup, so he could play four finals with us. This [final] was a very important game, as it allowed us to keep up at the top level.
Afterwards, Griezmann was asked about the continued speculation linking him with a move to Barcelona but opted against providing any details on what club he will be playing for next season.
"I hope he is happy with us. When I went I didn't think I could and after to I came back and the dreams could be achieved and this has been taught to me by the club and I will always be grateful".
"We hoped that he'd be at 100 percent and we gave him a fitness test this morning. If he stays we'll keep growing because we are destined to keep growing".
Atletico captain Gabi had memorably called the Europa League a "s-- competition" when his side surprisingly dropped into it from the Champions League in December.
"I left home when I was 14 wanting to win titles", he said after the match. "You see it every year and it's a joy to work with him because he looks for a person's weaknesses, tries to improve them and make them a more complete player", he asserted. "I owe a lot to Simeone and my team mates".
Marseille was going for a second European trophy, 25 years after winning the Champions League, but ultimately had no answer to Griezmann's mobility and finishing.
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