The midfielder moves to the Viola on a season-long loan with an option to buy.
The loan fee is set at €4m, with a further €12m due if the deal is turned into a permanent transfer.
Colpani posted a farewell to Monza and their fans earlier today: "Dear Monza, dear Brianza fans. We spent 4 years of battles and sweat together experienced on the pitch, disappointments and great joys that have brought us to where we are today.
"A path that started from Serie B, from the conquest of the latter, up to 2 years in the top flight with results beyond all expectations for a newly promoted team. Moments that will remain etched in my mind forever: the two victories against Juventus, against Napoli at home, at San Siro against Inter, and the great victory, last championship, against Milan.
"A special thank you to President Berlusconi and Dr. Galliani for the trust they have placed in me since the first day I wore these colours, the backbone of all our successes, our glue. And finally I thank my teammates for the fantastic group we have created on and off the pitch in these unforgettable 4 years. I have arrived as a boy and I leave you as a man because, together with you, this is what I have become.
"Thanks Monza."