The 22-year-old has joined the newly promoted Serie A side for an undisclosed fee.
The Slovakian international joined the Blues in 2008 and made his first team debut against Bolton Wanderers in the last game of the 2008/9 season.
In January 2010 Weiss joined Bolton Wanderers on loan until the end of the season, although most of his time there was spent on the bench.
Next up for the winger was a move to Scotland where he joined Rangers on loan for the 2010/11 season and in doing so claimed an SPL winners' medal.
The Slovakian had a successful season at Spanish side Espanyol last year and will most likely be remembered for scoring a spectacular goal from outside the penalty area during a 3-3 draw away at Atletico Bilbao.
The club wishes Vladimir every success at his new club and in his future career.