The France forward has signed a five-year deal, after the LaLiga champions agreed to trigger his €120million release clause.
Griezmann was seemingly set to join Barca in the summer of 2018, only to confirm during a television documentary he was staying at Atletico.
The 28-year-old forward signed a new contract with Atletico soon after, but reports surfaced in the second half of the 2018-19 campaign that he was hoping for another chance to join the Liga champions.
And the attacker acknowledged that U-turn in his first public comments since becoming a Barca player on Friday, saying he was taught as a child that opportunities can come around again.
“When I was a boy, my dad taught me that trains don’t come around just once.
“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,” Griezmann said in a video posted on Twitter by Barcelona.
