The France forward has signed a five-year deal after Barca agreed to trigger his €120million release clause.
Griezmann was seemingly set to join Barca last year only to confirm during a television documentary he was staying at Atletico.
✌️ Life is all about second chances. pic.twitter.com/5ArFiaP2ht— FC Barcelona (@FCBarcelona) July 12, 2019
And the attacker acknowledged that U-turn in his first public comments since becoming a Barca player on Friday.
"When I was a boy, my dad taught me that trains don't come around just once," Griezmann said in a video posted on Twitter by Barcelona.
"Now it's time to take on the challenge of a new destination. Finally, our paths cross.
"I'll defend the Barca colours with all my determination and commitment. It's our time."
The saga does not appear to be over, however, as Atletico are insisting Barcelona should have paid €200m to activate his release clause. They are arguing the France international agreed terms with Barca before his clause dropped on July 1.
"Atletico Madrid believes the termination of the contract occurred before the end of last season due to events, acts and demonstrations carried out by the player and that is why it [the club] has already started procedures it considers appropriate for the defence of its rights and legitimate interests," said the club's statement.