Coppola was sold by Verona to the Seagulls last week.
Bocchetti worked with Coppola last season and told the Athletic: "He is physically strong and reads the game very well, but he is also surprisingly fast for his size, a combination that makes him very effective in defence.
"He is a strong player. He arrives in the most prestigious league in the world and joins a great club. I am sure that, with his professionalism and open mind, it will be easy for him to improve further. This is certainly a big step forward in his career."
He also said: "Even some big Serie A clubs were interested, but I think this is the best choice for him, and also for Brighton.
"I am very attached to him, because I have seen him grow. I have nothing but positive things to say about him."