Griezmann drew criticism from both Barcelona and Atletico fans for revealing his decision in an hour-long documentary broadcast on Spanish TV station Movistar.
Atletico fought to keep Griezmann, who almost joined Manchester United last summer, according to Sky Sports’ Spanish football expert Guillem Balague.
Griezmann was offered £17.5m to stay and the promise of a £100m improvement of the squad in order to compete for next season’s top titles.
Thomas Lemar is set to be the first of those arrivals, with Atletico confirming they have agreed terms with the player and are the deal is now only subject to him passing a medical and finalising terms with Monaco.
The two clubs had reached a “preliminary agreement” over a deal for Lemar last week, Atletico said.
Griezmann, currently with the France squad at the 2018 World Cup, has now demonstrated his commitment to Atletico by adding another year to his contract after meeting with the club’s chief executive, Miguel Angel Gil Marin, in Russia.
Greizmann scored in France’s opening game of the tournament, a 2-1 win over Australia.
His team-mate for club and country, Lucas Hernandez, also penned a new deal until 2024 following the meeting.