The 32-year-old, who was born in the now-Kosovan city of Mitrovica, has made Udinese the sixth Italian club of his career following stints with Genoa, Hellas Verona, Lazio, Fiorentina and Napoli.
He made 44 appearances in all competitions for Watford but has opted against another season in the Premier League, instead signing a two-year contract at the Dacia Arena in Udine.
Udinese director Franco Collavino told the club website: "We wanted a player with his characteristics who already has experience in this league, and Behrami wanted to test himself in Serie A again.