Forestieri was a free agent after coming off contract with Sheffield Wednesday.
This is a return to Friuli for the 30-year-old forward, who already joined in 2010, eventually sold to Watford in 2013 after a series of loan spells.
“Forestieri is an old friend of Udinese," technical director Pierpaolo Marino told the club website.
“He left as a promising youngster and returns with the certainty he can give a strong contribution to the team. A player with his characteristics, creativity and finishing skills was missing from our squad."