The Slovakian youngster has called time on his spell with the Premier League champions, having made only one competitive appearance for them in the past four years
The 22-year-old leaves the Premier League winners for the newly promoted Serie A side after four years at the Etihad Stadium.
Weiss joined at the beginning of the 2008-09 season, making his first-team debut in the last game of the campaign against Bolton, whom he later joined on loan in January 2010 until the end of that term.
The Slovakian was loaned out again, this time to Rangers, for the entirety of 2010-11, picking up an SPL winners' medal.
And last year, Weiss had another successful loan spell with Espanyol in La Liga, but leaves City having only made one league appearance for his parent club.