Griezmann could sign off in style this weekend as Atletico host Eibar in their final league match of the season, needing just a point to finish ahead of Real Madrid for the first time since 2014.
"Griezmann today confirmed what he has been doing year by year".
"We hoped that he'd be at 100 percent and we gave him a fitness test this morning".
"It was a dream of mine to win a trophy with Atleti, with Simeone and with my team mates", Griezmann added.
Marseille began with urgency, but striker Valere Germain shot over from playmaker Dimitri Payet's slick pass after three minutes.
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Substitute Kostas Mitroglou almost pulled one back, his header coming off the post, before Gabi's low drive in the 89th minute made it 3-0.
The irrepressible Griezmann started and finished the move for his second, four minutes into the second half.
He celebrated both goals with an energetic celebratory dance from popular video game Fortnite, although he couldn't do it as well the second time around as he was quickly mobbed by teammates.
The captain was included in Rudi Garcia's starting XI after overcoming a muscle problem that had kept him out of Friday's 3-3 Ligue 1 draw with Guingamp.
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.
Griezmann and Diego Costa will lead Simeone's attack as Atletico returns to Lyon, where it lost 3-0 to Dynamo Kiev in the final of the now defunct Cup Winners' Cup in 1986.