Los Rojiblancos started slowly but took complete control of the match once Griezmann pounced on a mistake to net his first 21 minutes in.
Relive how the 90 minutes of action unfolded at the Groupama Stadium with Sports Mole's live text coverage below.
STARTING XI: Mandanda; Sarr, Rami, Luiz Gustavo, Amavi; Anguissa, Sanson; Thauvin, Payet, Ocampos; Germain
SUBS: Kamara, Lopez, Mitroglou, Njie, Pele, Rolando, Sakai
STARTING XI: Oblak; Lucas, Godin, Gimenez, Vrsaljko; Gabi, Saul, Koke, Correa; Costa, Griezmann
SUBS: Gameiro, Luis, Savic, Thomas, Torres, Juanfran, Werner
Rudi Garcia: "We have a lot of respect for Atletico. They are very solid, have the best defence in the Spanish League, and formidable attackers in Griezmann and Costa. The character of both teams is similar; we've shown this in the Europa League and also to get into a Champions League place. Atleti are one of the great teams in Spain. Perhaps they have more experience but this is a 90-minute football match - and that's it! But I'm disappointed Simeone is not on the bench. It's difficult for a coach to be deprived of being with his players."
Diego Simeone: "We are not thinking about [past final defeats], only what happens today. What happened before gives you experience and moments. There is a new moment that we are waiting on. Reality will dictate if we are worthy of the title. My absence? We lived it with Arsenal, at home, when German Burgos was [watching] over the team. Aside from the sadness that it gives me to not be there from the start in the final, I have a great feeling with German. We know each other for a lifetime, we have similar feelings and understanding of football."
MARSEILLE SUBS: Kamara, Mitroglou, Njie, Pele, Rolando, Sakai
ATLETICO MADRID SUBS: Gameiro, Luis, Savic, Thomas, Torres, Juanfran, Werner