The La Liga champions were said to have paid the Frenchmans €120m release clause earlier in July and the move has now been made official following an announcement from the Catalan giants.
Barca have confirmed that he has joined on a five-year deal, revealing the news in a statement on their official website.
It read: "FC Barcelona has paid the 120 million euro buyout clause to release Antoine Griezmann from Atlético Madrid. 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.
"We will shortly be publishing the full schedule for the presentation of Antoine Griezmann as a new member of the Barça first team."
The move has been the most talked about transfer during the current window and has been filled with plenty of dramatic twists.
The World Cup winner announced his decision to leave Atleti in May and an official announcement from Barca confirming the transfer was expected soon after.
However, the deal has dragged on, with Atleti accusing Barcelona president Josep Maria Bartomeu of tapping up Griezmann before reports emerged claiming the 2013/14 La Liga champions would fine the forward for failing to turn up to pre-season training.
The 28-year-old is expected to feature heavily alongside Lionel Messi and Luis Suarez, while Ernesto Valverde also has Ousmane Dembele, Philippe Coutinho and Malcom at his disposal.
Barca are looking to improve upon their 2018/19 season, during which they won La Liga with considerable ease but also lost the Copa del Rey final to Valencia and were knocked out of the Champions League by eventual winners Liverpool in the semi finals.