The Colombian completed a move to the Santiago Bernabeu from Monaco after starring for his country at the World Cup this summer, where he won the Golden Boot as he inspired them to the quarter-finals.
However, Cerezo feels that Griezmann, signed from Real Sociedad for around €25m, is more used to top-level football in Europe and believes he could be as influential for the club as new Barcelona signing Luis Suarez.
"Antoine is a player who is more tested across Europe and is the signing of the summer," he said at the Frenchman's unveiling.
"[Griezmann] is comparable to players like Luis Suarez. He's a great reinforcement for the club and we made a great effort to bring him in.
"Though he had many offers, he decided on a serious and important club like Atletico.
"We don't know about James because he still doesn't have a defined path."