The Italian side on Thursday confirmed the deal until June 30, 2019, without revealing whether there was an option to buy.
Both Watford and Udinese are owned by the Italian Pozzo family.
Zeegelaar arrived at Watford in the summer of 2017 from Sporting Lisbon but after playing 13 games last season has not featured this campaign.
The 28-year-old started his career at his hometown club Ajax in 2009, followed by spells at Spanish club Espanyol, Turkish side Elazigspor, Blackpool in England and Sporting Lisbon in Portugal.
Udinese are 15th in the Italian top flight, five points above the relegation zone.