"It is with a heart full of memories that I am closing this chapter of my life," France vice-captain Griezmann, 33, wrote on X.
Both players had indicated their desire to participate in the Paris Games, but their Spanish clubs -- Real Madrid where Mbappe, 25, is set to play next season and Atletico for 33-year-old Griezmann -- have said they will not release them.
Antoine Griezmann secured Champions League qualification for Atletico Madrid with a hat-trick in a 3-0 triumph at Getafe on Wednesday in La Liga.
Antoine Griezmann scored twice as Diego Simeone's men moved to within four points of their opponents and pulled five clear of fifth-placed Athletic Bilbao in the race for Champions League qualification.
Antoine Griezmann said Atletico Madrid will have to "suffer" at Borussia Dortmund to reach the Champions League semi-finals.
Atletico Madrid are hoping Antoine Griezmann's injury is nothing more than a sprained ankle after the forward was substituted in their 1-0 defeat by Inter Milan in the first leg of their Champions League last-16 tie, manager Diego Simeone said.
Antoine Griezmann became Atletico Madrid's all-time standalone top goalscorer with 174 goals after netting against Real Madrid in the Spanish Super Cup semi-final on Wednesday.
Griezmann's superb header after 64 minutes split the teams, although visitors Mallorca spurned some good openings in the final stages.
Antoine Griezmann struck a hat-trick in a 3-0 win over 10-man Celta Vigo to help Atletico Madrid climb provisionally second, in hot pursuit of their city rivals.
Atletico Madrid sealed top spot in Champions League Group D after second half goals from Frenchmen Kevin Gameiro and Antoine Griezmann gave them a comfortable 2-0 win at home to PSV Eindhoven on Wednesday.
Antoine Griezmann struck two goals, one in the 93rd minute, to give Atletico Madrid a 2-1 Group D win over Rostov on Tuesday that took them into the Champions League last 16 and preserved their 100 percent record.
Antoine Griezmann was Atletico Madrid's hero once more with the winner as last season's Champions League finalists moved third in La Liga with a 1-0 win over 10-man Deportivo la Coruna.
Antoine Griezmann should be considered a leading contender for the Ballon d'Or due to his performances in the last few months, according to Atletico Madrid coach Diego Simeone.
Antoine Griezmann deserved to be named UEFA's Best Player in Europe, according to Cristiano Ronaldo.
Antoine Griezmann deserves to be named UEFA's Best Player in Europe, according to Cristiano Ronaldo.
Losing a final to Cristiano Ronaldo has become an unfortunate habit for Antoine Griezmann and he is not happy about it.
Around 40 people are arrested in Paris after police use tear gas and water cannon against football fans hurling glass bottles at officers at the Eiffel Tower during the Euro 2016 final.
A 90th-minute header by substitute striker Antoine Griezmann and a stoppage-time special by Dimitri Payet secured France a heartstopping 2-0 win over Albania on Wednesday that sent the hosts through as the first team into the last 16 of Euro 2016.
Atletico Madrid forward Antoine Griezmann's 54th-minute strike ousts Bayern Munich from the UEFA Champions League as the Spanish side go through to the final on away goals.