The 29-year-old arrived in his native Spain on Thursday evening to undergo a medical, and he has since penned a contract with Celta Vigo that runs until June 2025.
Manquillo made a total of 110 appearances for Newcastle over a six-and-a-half-year period having arrived at the club from Atletico Madrid in the summer of 2017.
The right-back scored his solitary goal for the Magpies in a 4-1 defeat to Manchester United at Old Trafford in the Premier League in November 2021.
Manquillo departs Newcastle having not made a single appearance under manager Eddie Howe this season due to a series niggling muscle injuries.
Rafael Benitez, who signed Manquillo for Newcastle, has decided to reunite with the defender at Celta Vigo, who currently sit 16th in the La Liga table.
Manquillo becomes Celta Vigo's second signing of the January transfer window after midfielder Jailson, who joined the club from Palmeiras on a free transfer earlier this month.
It remains to be seen when Manquillo will make his debut for the Sky Blues as he is still recovering from adductor surgery.
Newcastle have allowed Manquillo to leave St James' Park, as Howe already has three senior right-back options at his disposal in Kieran Trippier, Valentino Livramento and Emil Krafth.
However, reports have recently emerged claiming that Bayern Munich hold an interest in Trippier, who is allegedly open to joining the German giants this month.
Newcastle are said to have rejected Bayern's initial loan offer with an obligation to buy for Trippier, as they have no interest in parting ways with the 33-year-old this month.
The Magpies, who sit ninth in the Premier League table, are also understood to have turned down a loan offer from Atletico Madrid for striker Callum Wilson.