The French World Cup winner will be presented as a Barcelona player in the coming days and the forward will sign a five-year deal, with his new contract carrying an €800m (£717m) buyout clause.
It was reported on Thursday that Barcelona were set to pay Griezmann’s £108m buyout clause, which the Spanish champions have now done.
It draws to a close the transfer saga involving the France forward, which has been rumbling for well over a year.
Griezmann decided last summer to prolong his stay at Atletico, revealing his decision to snub Barca’s offer in a documentary which stoked tensions between the player and the club – not least because it was made by the production company owned by Barca defender Gerard Pique.
He signed a new deal with Atletico until 2023 containing a buy-out clause of €200m (£179m), which dropped to £108m on July 1 2019.
The former Real Sociedad forward departs Atletico after five prolific seasons in the capital, which saw him score 133 goals as well as helping the club win the Europa League, UEFA Super Cup and Spanish Supercopa.
Griezmann’s task will be to help Barcelona win the Champions League for a sixth time.
Their last European title was in 2015, and the team collapsed in the second leg of last year’s semifinal when Liverpool overturned a 3-0 loss by dealing Barcelona a humiliating 4-0 defeat.