Argentine striker Lautaro Martinez, who was close to being signed by Atletico earlier this year but who opted to play for Inter Milan, scored the winning goal on Saturday.
Griezmann revealed his decision while preparing for the World Cup in Russia. France plays its first match against Australia on Saturday.
It was an intensely emotional ending for the players who were key members of Spain's golden generation that won two European Championships and a World Cup.
Atletico Madrid players paraded through the Spanish capital on Friday to celebrate the team's Europa League triumph.
Real Madrid plays Villarreal in the final round of the Liga before the Champions League final on May 26 in Kiev.
Rafael Nadal appeared with a Atletico Madrid jersey during the club's Europa League match against Arsenal last week.
The result also meant Arsenal will not qualify for the Champions League for a second straight season.
The winner between Madrid and Arsenal will likely play Marseille, who beat Salzburg 2-0 in their first leg with goals from Florian Thauvin and Clinton N'Jie.
Atletico, the 2010 and 2012 winner, will travel to London for the first leg against Arsenal who have never won the Europa League or the UEFA Cup.
The draw benefitted FC Barcelona as the league leaders have an 11-point lead over Atletico at the top of the standings with seven matches left.
Kevin Gameiro converted a first-half penalty kick as Atletico defeated Deportivo La Coruna 1-0 on Sunday to move within nine points of leader Barcelona with eight matches remaining.
Marseille progressed after a 2-1 win at Athletic Bilbao that was marred by crowd trouble. Lazio advanced with a 2-0 win at Dinamo Kiev and Leipzig drew 1-1 at Zenit.
There was another surprise in Germany where two goals from Valon Berisha led Salzburg to a 2-1 victory at Borussia Dortmund.
It was Messi's sixth goal from a free kick this season and his third straight after successful free kicks against Girona and Las Palmas.
Barcelona, which has drawn three of its last five league matches, will host Atletico on Sunday needing to halt an eight-match winning streak by Diego Simeone's team.
There was a minute of silence before matches to honor former Barcelona and Sporting Gijon striker Enrique Castro "Quini," who died of a heart attack on Tuesday. He was 68.
The FC Barcelona and Griezman links have been joined since the start of the summer despite the Blaugrana successfully bringing in Ousmane Dembele and Philipe Coutinho.
Athletic Bilbao are scheduled to next face Marseille, while Borussia Dortmund will take on Austrian side Salzburg.
Shockingly, Serie A leaders Napoli weren't good enough to advance in the Europa League on Thursday after they were knocked out in Germany by RP Leipzig.
Coach Diego Simeone, a longtime supporter of Fernando Torres, says he will not go out of his way to try to keep the former Spain striker.
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