The striker has joined on loan with an option to buy from Napoli for a total package of around €40m.
“I’m very proud to wear this important, historic shirt and playing in the Premier League is an honour for me,” he told Forest's website.
“It’s an honour that the club and the staff have given me this opportunity and I hope to pay them back for their trust with lots of goals.
“I’m well aware of this club. I wanted to come, they wanted me a lot, so it was a choice from the heart because I really wanted to come here and I want to give everything for the team, and most importantly, to be helpful for the whole group.
“As I said before, as soon as Nottingham Forest called me with the chance to play in the Premier League, it was my first choice because playing in the Premier League has been a dream of mine since I was a child. And again, I want to thank the club and all the staff for giving me this chance.”
Asked about his qualities Lucca added: “I’m a hungry player, willing to prove myself, score goals and help the team win as many games as possible.”