Atletico is looking to win the Europa League for the third time in nine seasons, after triumphing in 2010 and again in 2012, shortly after "Cholo" Simeone was appointed coach.
He also played a part in the build-up to Gabi's late goal that sealed the victory.
But the France global is linked with a move to Barcelona in the close-season despite being contracted until 2022. "I hope I can continue to win more trophies". "I want to enjoy the moment".
Griezmann's decisive contribution helped erase bitter memories of 2016, when he missed a second-half penalty in Atletico's Champions League final loss to Real Madrid. "I owe a lot to Simeone and my team-mates".
"He has played three finals with us, has won two, and so that shows that he is not far away from his objective of regularly playing finals".
"I am proud of the season Marseille have had, of their fans who on their own nearly filled the whole stadium, and of (coach) Rudi Garcia and what he has done with that team". I had lost finals, I left home at 14 to win titles and today I had the chance to win a trophy.
"I'm really happy, proud of what I have done this season", he said.
He scored his first on 21 minutes, seizing on an error from Andre Zambo Anguissa to slide the ball into the net, and he scored his second shortly after the break, exchanging passes with Koke and then chipping the ball over the onrushing Steve Mandanda.
Atletico Madrid's Gabi and Fernando Torres lift the trophy as they celebrate winning the Europa League against Olympique de Marseille, at Groupama Stadium, Lyon, France, on Wednesday, May 16, 2018.
The winners of the Europa League are awarded direct qualification for next season's Champions League group stage.
Marseille were the better side for large portions of the game, but when star man Payet was forced off early in the first half and Griezmann took advantage of the error at the back, it was always going to be a tough game.