The Italians have acquired the club from Laurence Bassini, who bought the Hornets 15 months ago when he fronted Watford FC Limited's £440,000 takeover.
Administrator Andrew Andronikou, who advised the Hornets on the sale, said: "We are delighted to have ensured that Watford's immediate future is safe.
"The family have a proven track record of building successful teams on the field, and balancing the books off it."
Andronikou added: "This transaction is a significant one, as it provides the Pozzo football dynasty with a secure platform to introduce its successful formula to the UK."
Giampaolo Pozzo has owned Serie A side Udinese since 1986 and bought Spanish La Liga outfit Granada three years ago, but his son Gino is expected to take charge at Vicarage Road.
Former West Ham boss Gianfranco Zola is known to be admired by the Pozzo family, who have also been impressed with the Championship club's youth academy set-up, and they are giving strong consideration to recruiting the Italian as manager for next season.
Current Watford manager Sean Dyche led the club to their highest league position for four years in his debut season, but is said to be "aware of the situation".
Former West Ham chief executive Scott Duxbury is also likely to accept a role within the new regime at Vicarage Road.
Duxbury and Zola have a strong relationship from their days at Upton Park, but it remains to be seen if they will link up again at Watford.
A week ago the Hornets denied claims by Bassini that the takeover deal was off.
His tenure at Vicarage Road has seen the club exceed expectations under Dyche, but Bassini has been reluctant to face the media and had a public fall-out with former chairman Graham Taylor.
Watford have been taken over by Udinese and Granada owners the Pozzo family.