The former Atletico Madrid forward was denied his regular number when he arrived at Barcelona in July 2019, as it was held by Philippe Coutinho, and he agreed to wear the 17 shirt instead.
\But with Coutinho having since gone on loan to Bayern Munich for last season, and with question marks over whether the winger will stay at Barcelona for the new campaign, the Brazilian has ceded the number to Griezmann.
On Instagram, Griezmann wrote: "It is an honour to wear the 7 at Barca!"
He added: "I want to say thank you to @phil.coutinho, who as well as being a great player is a big friend."
The number switch was announced by Barcelona on their social media accounts, with a video featuring Brooklyn Nets NBA star Kevin Durant opening a box containing Barcelona number seven shirts bearing his name and that of Griezmann.
Griezmann scored 15 goals in 41 games for Barcelona last season but often faced criticism for his performances as he struggled to make the greater contribution that many expected of him.
He has previously worn the number seven with Real Sociedad, Atletico Madrid and France, donning the number during their run to World Cup glory two years ago in Russia.