Griezmann signed a five-year deal with Barca after the LaLiga champion triggered the €120 million ($193.5 million) release clause in his Atletico Madrid contract.
Speaking ahead of his official unveiling, Griezmann indicated he is keen to get on the pitch with Barca captain Messi.
"Very happy and looking forward to seeing what Messi is like on a day-to-day basis in training," the Frenchman said. "Playing next to him is an incredible joy.
"For me, it's a big club and I hope to help it continue being big - or even get even bigger. I'm really looking forward to working with my new team-mates and with the boss and playing at Camp Nou and hopefully winning a lot of trophies.
"I like to have fun on the field and off it, in the dressing room. I like to play with joy and I hope to bring a lot of joy to my team-mates and the fans. I hope we have fun together."
Griezmann will undergo his medical on Monday (AEST) before a formal presentation and media conference, with the France forward thrilled to be reuniting with international team-mates Samuel Umtiti and Ousmane Dembele.
"I'm very happy and very excited, looking forward to working with the squad and meeting my new team-mates, so very happy," he added.
"A new challenge, new targets. Important things and I hope I can do as well as I can as I have been doing for my club and country.
"With Sam and Ousmane, I have a very good relationship with both of them. I'm looking forward to seeing them."