The deal will cost Atletico up to £4.4m, which Cerezo believes is a "very low price" considering how long the club have been chasing him.
"Many Spanish and foreign teams would have sacrificed a lot to have Villa in their squads and we have paid a very low price for him, so we're very pleased about that," Cerezo told Radio Nacional de Espana.
"The most important factor in the deal was that we have wanted to sign Villa for a long time and that's why we're so happy. We wanted to sign him when he went to Valencia from Zaragoza, and now he belongs to us.
"Villa still has many seasons left in football. He is a natural goalscorer. We are expecting great things from him because he is one of the key players in the Spain team. We expect him to score many goals."
Villa was at Barca for three years before making the move to Atletico.