The 26-year-old scored six goals and provided six assists across 34 appearances during his loan season in Friuli, a return that convinced Udinese to make the move permanent.
According to journalist Fabrizio Romano, Udinese have paid around €5 million to Galatasaray, with the Turkish club retaining the right to 50 per cent of any future sale.
Zaniolo has signed a contract with Udinese running until June 2029.
Galatasaray paid €15 million to sign Zaniolo from Roma in the winter window of the 2022-23 season, but his time in Istanbul never produced the consistency many had expected when he arrived.
A series of loan spells followed as Zaniolo struggled to establish himself, taking in stints at Aston Villa, Atalanta and Fiorentina before his move to Udinese finally provided the stability his career had been missing.
Galatasaray issued a farewell statement thanking the player for his contribution during his time at the club.
"Galatasaray would like to thank Nicolo Zaniolo for his efforts and contributions while wearing the Galatasaray jersey, and wishes him success in the rest of his career," the statement read.
Zaniolo also posted a message of his own on social media, expressing gratitude towards the club's supporters.
"Thank you very much for the unconditional support you have given me all these years. You will always be a part of me, and from today I will be one more of your fans! Thank you, Galatasaray."
According to Sky Sport Italia, Zaniolo and his agent Claudio Vigorelli expressed some disappointment that a contract renewal with Galatasaray had not materialised as the player and his camp had hoped, before the move to Udinese was confirmed as permanent.
Born in Massa, Zaniolo came through the Italian football system and has represented a notably varied list of clubs throughout his career, including Inter Milan, Roma, Aston Villa, Fiorentina, Galatasaray and now Udinese on a permanent basis.
He has also earned 19 caps for the senior Italy national team, scoring twice, a record that reflects the talent that once made him one of the most highly rated young players to emerge from Italian football.
For Udinese, securing Zaniolo on a permanent deal represents a low-cost gamble on a player whose career has been defined as much by setbacks as by moments of real quality.
Having found his form again in Friuli, Zaniolo now has the long-term security of a contract that gives both player and club the chance to build on a productive first season together.