The Frenchman, who was born just 70 kilometers from the final venue, scored goals either side of half time, before captain Gabi put the icing on the cake with a third late on.
Marseille started the game well and were unfortunate to see a Kostas Mitroglou header hit the post in the second half, but the French side were comfortably second best all night.
If this was to be Griezmann's final game in an Atletico shirt -- the forward has suitors from all over Europe -- then he certainly made it one for the fans to remember.
As the players emerged onto the pitch, barely visible through the thick smoke of flares let off by the Marseille fans, the ground rumbled with expectation.
Although this Atletico side boast vastly more European experience than their French opponents, it was Marseille who started the better.
The first chance came within minutes, swiftly carving open an uncharacteristically static Atletico defense, which has been the stingiest in Europe this season.
A neat interchange between Dimitri Payet and Florian Thauvin culminated in the former sliding an inch-perfect through ball into the path of Valère Germain, but his shot was skewed horribly wide of the goal.
The Ligue 1 side continued to press, clearly buoyed by the audibly pro-Marseille crowd -- the final being played just 300 kilometers away in Lyon -- and center back Adil Rami spun and cracked a shot narrowly past the post.
Each club had been given an allocation of 11,500 for the final -- a paltry number criticized across Europe -- but you got the sense many thousand more Marseille fans, by hook or crook, had managed to get their hands on extra tickets.
Their players seemed to be feeding off the early energy, in particular Bouna Sarr down the right, who was proving a real handful for Atleti left back Lucas Hernández.
Sarr had suffered a dislocated shoulder just five days earlier in the draw against Guingamp, but it was clear why Marseille had been so eager to quickly patch him up to return to action.
Atletico had barely got a foothold on game but, as the clock struck 20 minutes, they somehow found themselves in front.
Marseille goalkeeper Steve Mandanda passed the ball short to Zambo Anguissa, but the defender's horror touch allowed Gabi to play the ball through to Griezmann, who coolly sat Mandanda down and slid the ball to his right.
The boy from Macon, a town just 70 km away from Lyon, had returned with a bang to the shores he was forced to leave as a child, deemed too small to make it as a footballer in France.
That goal appeared to suck the belief out of Marseille and they were dealt a swift double blow when captain and talisman Payet was forced off with a recurrence of a hamstring injury soon after.
Atleti now had their opponents where they wanted them and Marseille, having spent the past 10 minutes chasing shadows, were grateful to hear the half time whistle.
But if they felt the break was welcome respite, their evening was only going to get worse soon after the restart.
Marseille, again the masters of their own downfall, gave the ball away inside their half, allowing Koke to play a ball through to Griezmann.
The Frenchman took two touches with his left foot, the first an exquisite drag to bring the ball under his control, before dinking a delightful finish over the onrushing Mandanda.
Despite there being more than half an hour left to play, that, you felt, was that. With Payet off the pitch, Marseille looked bereft of ideas as they tried to break down Atleti's expert defense.
There seemed a lack of hope, as well as quality, every time Marseille got into the final third, constantly gifting Ateltico possession and allowing them to counter.
Griezmann continued to steal the show, his deft touches and fancy flicks were too much for the Marseille defense, wriggling through challenges at will.
Although Marseille's players had seemingly given up, having been given the runaround by the French star, their fans certainly hadn't.
The noise again became deafening and Marseille pressed forward in one final attempt to get back into the game.
Sarr's terrific cross into the box was met by the head of substitute Mitroglou, but the Greek forward looked on in disbelief as the ball hit the post and somehow spun away from goal.
But any lingering hope was soon extinguished, as Atleti captain and stalwart Gabi drove home a third goal with just three minutes remaining.
With the trophy now within their grasp, Atletico's current golden boy, Griezmann, was then substituted for the club's former.
On came Fernando Torres, the boyhood Atleti fan with more than 400 appearances for the club, to celebrate his first ever major trophy for the club he used to support from the stands as a kid.
Torres will be leaving at the of the season, his contract for his second spell at the club not being renewed. As fairytale finishes go, it's not a bad way to bow out from the club he loves.