The 27-year-old France worldwide has been heavily linked with a move away from the Wanda Metropolitano this summer and showed his class as Atleti ran out comfortable 3-0 winners in Lyon.
"It was a dream of mine to win this trophy with my teammates and with Simeone", the France forward said. "I owe a lot to Simeone and my team mates".
With Liverpool fans hoping for any possible advantage over Madrid ahead of their showdown on May 26, fans are praying none of Jurgen Klopp's players "jinx" the side as Payet appeared to. The star of the 2016 European Championships - he won the tournament's Golden Boot for scoring most goals - has returned to top form of late and he ruthlessly ended Marseille's hopes of winning their first continental title since their shock Champions League win in 1993. "I want to enjoy the moment".
Marseille had wasted a chance to take a fourth-minute lead when Valere Germain skewed his shot wide with only Jan Oblak to beat.
AFP Getty Images Olympique de Marseille's fans riot in the Vieux Port in Marseille
"I am proud of the season Marseille have had, of their fans who on their own nearly filled the whole stadium, and of (coach) Rudi Garcia and what he has done with that team". "In the second half they raised their level and the best team won".
Victory for Atletico, who have already qualified for the Champions League, means the automatic group-stage berth will go to third place in France, a spot in which Marseille could still finish. "It represents the value of hard work, a steady hand and consistency, values to be successful in life". I had lost finals, I left home at 14 to win titles and today I had the chance to win a trophy.
Four minutes after the re-start, Koke ran into a hole in the Marseille midfield and slipped the ball to Griezmann who dinked the ball past Mandanda.
He got the opener midway through the first half and then netted a superb second four minutes after the break.
But nothing could disguise Atletico's vast superiority, as it added to its Europa League trophies from 2010 and 2012. It also lost another Champions League final to Real Madrid in 2014 and the gulf in experience was evident.
Allan McGregor completes move back to old club
Scott Arfield agreed a four-year deal at Ibrox earlier this week, with the 29-year-old joining after his contract at Burnley had expired.