Donnarumma, 26, made the move from Champions League holders PSG to Man City in the dying stages of the summer transfer window for a reported fee of £25 million.
The Italy captain played a key role in the French side’s tournament win, and he already has his sights set on retaining the trophy with City.
“It is one of our goals, I’m not going to hide it,” he said. “Lifting the Champions League trophy with City would be a dream for me. I think the Champions League is the best trophy for a football player. It was an indescribable emotion.”
He added: “I hope to get as far as possible in the Champions League. We have the game against Napoli, which is a difficult one, however all games are difficult. Napoli have a strong team. I know them, I have a lot of friends there.”
He could be set to make his debut in the Manchester derby on Sunday and has already vowed to make history with his new club.
He explained: “The fact that he wanted me here is a reason to be proud of. It's an indescribable emotion. Being coached by him is the best for a football player. I can't wait to follow him and take to the pitch with him.
“I'm sure he will help me a lot and we will do great things together, this season as well as in the following years. I think his history speaks for itself. It’s been an era of unbelievable success here.
“I'm proud to be here and happy about the choice I've made and I hope I will make history here and win as many trophies as possible, that is my goal.
“It’s a new chapter in my life and my career. I'm ready for this challenge. I've always dreamt about playing in the Premier League as it's the best league in the world.”