The 26-year-old goalkeeper joined the Whites in the summer of 2014 from Chievo and went on to make 98 appearances for the club, during a three-year spell.
However, after the arrival of Felix Wiedwald for £500,000 from Werder Bremen he was further pushed down the pecking order at Elland Road behind Wiedwald and Rob Green.
Silvestri left United’s Austrian training camp today to fly to Italy and he has completed a move for an undisclosed fee.
A statement on the club’s website read: “We would like to thank Marco for his services and wish him good luck in the future.
“Fellow Untied goalkeeper Bailey Peacock-Farrell has now linked up with the first team squad in Austria.”