The 28-year-old World Cup winner has signed a five-year deal which includes an 800m euro (£717m) release clause.
He signed a new five-year deal in June 2018, but announced in May he would be leaving the club this summer.
Atletico have been unhappy about Barcelona’s approach for the player and say 120m euros is “insufficient”.
Griezmann is now the the world’s sixth most expensive signing behind Neymar, Kylian Mbappe, Philippe Coutinho, Joao Felix and Ousmane Dembele.
A transfer saga
Shortly after Barcelona announced the signing on Friday, Atletico responded by saying his buyout clause should have been 200m euros (£179m) – the value at the time they believe Griezmann and Barcelona began negotiating.
“Griezmann, represented by his lawyer, has appeared at the headquarters of the Professional Football League to unilaterally terminate the contract that links the player with Atletico, with Barcelona having deposited the sum of 120m euros in the name and on behalf of the footballer,” they said in a statement.
“Atletico believes that the amount deposited is insufficient to meet its rescission clause, since it is obvious that the commitment of the player and Barcelona was closed before the aforementioned clause was reduced from 200 to 120 million euros.
“Atletico believes that the termination of the contract happened before the end of the last season due to facts, acts and demonstrations made by the player, and therefore has already initiated the procedures it has deemed appropriate to protect their rights and lawful interests.”
Atletico reported Barcelona to Fifa over an alleged illegal approach for Griezmann in December 2017.
Griezmann then rejected an offer from Barcelona last year and revealed his thought process in a documentary called The Decision.
But earlier this month Atletico accused Barca and Griezmann of disrespect and claimed the La Liga champions talked to their forward in March. They also ordered the player to report for pre-season.
In a statement, the Madrid club expressed their “strongest repulsion for the behaviour of both, especially Barcelona”.
Who is Griezmann?
Griezmann joined Atletico Madrid from Real Sociedad in 2014 and scored 133 goals in 256 appearances.
The Frenchman won the Europa League, the Spanish Super Cup and the Uefa Super Cup during his time at Atletico and was the team’s top scorer in each of the last five seasons. While
He was top scorer at Euro 2016 and chosen as best player of the tournament as France finished as runners-up to Portugal. That season also saw him finish third in the Ballon d’Or behind Lionel Messi and Cristiano Ronaldo.
“With his arrival at Barcelona, the Frenchman takes another step forward in his career with the goal of consolidating his place as one of the best players in the world,” said the Catalan club.
He becomes Barca’s fourth major signing of the summer, following the acquisition of midfielder Frenkie de Jong from Ajax, goalkeeper Neto from Valencia and defender Emerson from Brazilian side Atletico-MG. It takes their spending this summer to 233m euros (£199.7m.)
He joins a star-studded forward line at the Nou Camp of Messi, Luis Suarez, Dembele and Coutinho, while Paris St-Germain forward Neymar has also been linked with a return to the club this summer.
Atletico finished second in La Liga last season, nine points behind Griezmann’s new club.
Griezmann the NBA fan
- Barca’s latest signing was initially rejected as a footballer before reaching his teenage years for being too small
- Griezmann is an NBA fanatic and his favourite player is Derrick Rose of Detroit Pistons
- Griezmann’s house in Madrid has a basketball court for him to practice
- The Frenchman is a lover of Uruguay and its culture after being influenced by team-mates from the country
La Liga clubs splash the cash
Griezmann’s signing means that three of the top 10 most expensive transfers of all-time have all taken place this summer.
Atletico Madrid spent 126m euros to buy 19-year-old Portugal forward Felix from Benfica earlier this month.
Real Madrid signed Belgium forward Eden Hazard from Chelsea in June for a fee that could eventually exceed £150m. The 13-time European champions, who finished third in the league last season, have spent close to £300m this summer.
They also signed Serbia striker Luka Jovic from Eintracht Frankfurt for £53m, left-back Ferland Mendy from Lyon for £47.1m, Porto defender Eder Militao for £42.7m and Brazil forward Rodrygo who joined from Santos for £40m.