The 29-year-old has made just three appearances for the Hornets this season, and boss Javi Gracia was happy for him to move on to get more game-time under his belt.
The Serie A outfit are delighted with the move, with technical director Daniele Prade hailing the four-cap Italy forward as a potent addition to the club's forward line.
"Okaka is a strong point physically, good at defending the ball and getting the team up," Prade told Udinese's official club website. "Stefano is strong in the air and inside the penalty area."
Okaka has been at Watford since the summer of 2016, but has struggled for opportunities under Gracia and will be hoping to get his career back on track with the Italians.