The France international is back under Diego Simeone two years after joining the Blaugrana for £108m
Atletico bring the 30-year-old back to the Spanish capital two years after selling the player for £108 million in 2019 to the Camp Nou.
In a club statement Atleti said the deal includes an option for either club to extend the loan arrangement by a year.
Barca’s statement also added that the deal contained an obligation to buy Griezmann, with LaLiga champions Atletico also paying the player’s wages in full.
Local media reports in Spain put the purchase option at €40m (£34m).
The deal had been thrown into doubt with neither side announcing the move before the midnight CET deadline.
Local media said the delay was caused by a problem with LaLiga’s transfer registration system, but the league confirmed they had received all relevant documentation in time and had not granted an extension for the deal to be completed.
While Barcelona moved the France international on, they replaced him with Sevilla to sign Dutch forward Luuk de Jong on a season-long loan deal with the option of a permanent transfer, the club said in a statement on Wednesday.
De Jong, 31, arrives at the Nou Camp after two seasons in Andalucia, where he helped Sevilla to the 2020 Europa League crown and scored 10 goals in 69 LaLiga appearances.
The move capped a busy deadline day for Barca, who sanctioned the departures of Emerson Royal to Tottenham Hotspur, Rey Manaj to Spezia and Ilaix Moriba to RB Leipzig.
Barca also announced they had registered Sergio Aguero after first teamers Jordi Alba and Sergio Busquets agreed to a wage reduction for this season and the deferment of payments for the following years of their deals.
Reuters contributed to this report