The full-back returns to his native Spain following six-and-a-half years at St James' Park, having arrived from Atlético Madrid in July 2017.
Manquillo made 110 appearances in all competitions for the Magpies, with his solitary goal for the club coming away to Manchester United in 2021.
The 29-year-old will now link up with former boss Rafa Benítez, whose side currently sit 16th in the La Liga table.
Newcastle United would like to thank Javier for his service and everybody at the club wishes him well for the future.