The 27-year-old Cameroon right-back never played for the Italian side in six years, spending the entire time on loan with Spanish club Granada.
Thirteen members of Watford's current squad have played for Granada, Udinese or both - with all three sides owned by Giampaolo Pozzo.
Nyom was part of the Cameroon squad at last summer's World Cup finals, playing in the 4-1 defeat by hosts Brazil.
He is Watford's seventh signing of the summer after they were promoted to the Premier League in May.
Nyom was still in contract at Udinese with no details of a transfer fee being revealed.
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Watford have signed defender Allan Nyom from Udinese on a four-year contract.