And Atletico's captain, Gabi, put the icing on the cake by firing in a third in the 89th minute.
As he now looks towards World Cup success with France, Griezmann was pleased to lift a trophy under Atleti boss Diego Simeone.
Madrid's win in Lyon brings the tally of European trophies won by Spanish sides to eight of the past nine - Manchester United's triumph in the 2017 edition of this tournament is the only exception.
"I've been with Atleti for four years and now I have a strong bond - with my team-mates, with my fans".
The BT Sport app will be carrying a free Marseille v Atletico Madrid live stream from this time onwards, with both platforms showing the game on the revolutionary enhanced video player. I have no doubt that there are certain things that could make it more likely that he stays. "It made us realise what the team was capable of, and five months ago a lot of the players were being seriously questioned".
Atletico Madrid’s Fernando Torres and team mates celebrate with the trophy after winning the Europa League
Marseille was lost without the silky playmaker pulling the strings in midfield, and Atletico took complete control after he went off in the 31st minute. "He was decisive in the most important moment in the game", Simeone told a news conference. We also missed him from set-pieces as Atletico, if they do ever concede, sometimes concede from set-pieces.
"I have a great communion with my players and I can be at home or in the hotel but they will still play the same way", the 48-year-old manager added. Without Payet's threat, Atletico's midfield was able to push up much more, less anxious about protecting the space behind them. But the prospect of him travelling to Russian Federation while not fully fit is not an enticing one for Deschamps. "In matches like this you have to take risks".
The French side should have been in front inside the opening 4 minutes with Payet teeing up Germain who fired wide.
Even so, Marseille were agonisingly close to dragging themselves back into the match when a header from Kostas Mitroglou hit the inside of the post and bounced across the face of Oblak's goal to safety.
"We let our chance go in the first half".More news: Margot Kidder, Lois Lane in 'Superman', dead at 69