The deal also includes an €800m release clause.
The France global becomes Barca's third signing of the summer, following the arrivals of Frenkie de Jong and Neto.
Griezmann failed to show up for his side's pre-season gathering on Sunday after he had announced in May he would be leaving the Wanda Metropolitano but could not reveal his destination until his release clause dropped from €200 million to €120 million on July 1.More news: Modern man came earlier to Europe than assumed
Click through the gallery above to see seven players who could soon leave Barca, according to Sport. The two clubs met in Madrid last Thursday but it quickly became apparent that Atletico would not accept a payment plan.
After Barca president Josep Maria Bartomeu confirmed the meeting had taken place, the Rojiblancos released a strongly worded statement criticising both Barca and Griezmann's actions. He didn't and was subsequently fined.More news: Amazon's Alexa will offer medical advice to United Kingdom users
He rejected an offer from Barcelona a year ago and revealed his thought process in a documentary called The Decision.
"The player will sign a contract with his new club for the next five seasons, through to 30 June 2024, with a buyout clause of 800 million euros".
Griezmann's buyout clause dropped from £180m to £108m on July 1 and L'Equipe have now reported that Barcelona have finally stumped up the cash for the 2018 World Cup victor.More news: Black Caucus Member Charges AOC With Using the Race Card
Griezmann will be calling time on his five-year career at Atletico, after joining from Real Sociedad in 2014.