The 27 year old, who faces a summer of speculation over a move away from the Wanda Metropolitano, scored in each half – with Gabi striking late on to seal a 3-0 win for Atleti.
Coach Diego Simeone watched on from the stands having been hit with a four-game ban for being sent off during the semi-final first-leg at Arsenal but still saw his side ease to victory.
Rudi Garcia’s Marseille side did not create enough to break down one of Europe’s toughest defences and their chances of causing an upset took a blow with Dimitri Payet limping off injured in the first half.
Griezmann, who scored in every knockout round for Atleti after they dropped down from the Champions League, proved to be the difference with two smart finishes more than enough to seal the trophy.
The French side should have been ahead inside the opening four minutes with Payet feeding Valere Germain, who could only fire wide when through on goal.
Adil Rami shot wide shortly afterwards and the Ligue 1 outfit were more than holding their own until they all but gifted the opener to Griezmann.
Zambo Anguissa could not control Steve Mandanda’s ball out from the back and Atleti pounced, Gabi nipping in to play in Griezmann, who finished coolly to put Simeone’s men ahead.
Marseille’s chances took a blow when captain and talisman Payet was forced off with a little over half an hour on the clock.
The former West Ham man had been struggling with a muscle injury ahead of the final and was in tears as he made way for Maxime Lopez.
Griezmann doubled the advantage less than five minutes after the interval, Koke providing the assist for a clever dinked finish for the France forward.
Diego Godin headed over a Griezmann corner shortly afterwards as the La Liga side started to dominate proceedings.
Marseille were struggling to create the chances required to reduce the arrears as Madrid started to kill the game in a manner they are renowned for, although substitute Kostas Mitroglou hit the post with a header.
Skipper Gabi added a rare goal late on to secure a comfortable night at the office for Atleti, who brought on Fernando Torres in stoppage time for his final appearance for the club.