The 23-year-old stopper joins the Championship club on a four-year contract for an undisclosed fee from Chievo.
Speaking of Silvestri, Leeds manager Dave Hockaday told the club website: "Everybody in Italy believes that Marco is destined for very big things. We are delighted to welcome him to Leeds.
"He has been training with us for a week now and he has impressed everybody. Not only with his quality on the park but with his general manner off it as well."
Silvestri is Leeds's second signing of the summer, following another goalkeeper's arrival - Stuart Taylor - last week.