It is Griezmann's first major title with Atletico, and a fitting way to bow out if he leaves at the season's end, with Barcelona tipped as his next destination.
Griezmann -- brought up in Macon, just 70 kilometres from Lyon -- scored once in each half, his lethal finishes coming either side of Marseille losing Dimitri Payet to injury, the French team's captain coming off in tears.
Griezmann now has 29 goals this season, although it was Gabi's late strike that sealed the victory.
"This is a reward for me after I left home aged 14, for all the work I have put in, the suffering," said Griezmann, who has spent his whole career in Spain but had only previously won one Spanish Super Cup.
Atletico's triumph comes after agonising defeats to Real Madrid in the Champions League finals of 2014 and 2016. They had previously won the Europa League in 2010 and again in 2012, the latter coming just six months after Diego Simeone's appointment as coach.
Simeone, who had to watch from the stands due to a touchline ban, called the victory a reward for his side's hard work and even expressed hope that Griezmann could be convinced to stay.
"This was just confirmation of what Griezmann has been doing year after year," said the Argentine.
"I hope he is happy with us. I have no doubt that there are certain things that could make it more likely that he stays.
"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.
"We are not far away in sporting terms from teams who are more powerful than us."
Marseille had been desperate to win the second European trophy in their history, on French soil, 25 years after beating AC Milan in the inaugural Champions League final.
But it was a flat night for their huge support, who threatened to ruin the occasion by lighting flares and setting off firecrackers at one end of the stadium, with some even being thrown onto the pitch towards the end.
The game carried on regardless, with Rudi Garcia's side well beaten.
"We let our chance go in the first half. Firstly, we had the best chance to go ahead, and secondly an error from us meant we fell behind," said Garcia.
"The scoreline is harsh but the better team won."