The Spanish side, who finished fourth in La Liga last season and are managed by former Spain coach Julen Lopetegui, are believed to covering Telles' wages in full and that the deal does not include an option or obligation to sign the Brazil international.
The 29-year-old joined the Old Trafford giants from Porto in October 2020 and made 50 appearances in all competitions for the Red Devils.
The globetrotting Telles will now play in a sixth country after starting his career with Juventude and Gremio in his native Brazil, before moving to Galatasaray in Turkey, Italy's Internazionale in Italy, Porto in Portugal and Manchester United in England.
Telles has mostly played back-up to Luke Shaw and was pushed further down the pecking order by the summer arrival of Feyenoord's Tyrell Malacia.
Brandon Williams has also returned to the club after spending last season at Norwich and Telles has joined Sevilla on loan for the 2022-23 campaign.
Telles becomes the latest player to leave Erik ten Hag's new-look United.
Paul Pogba, Edinson Cavani and Jesse Lingard left at the end of their contracts, as did Nemanja Matic and Juan Mata.
Andreas Pereira has joined Fulham on a permanent deal, while Dean Henderson and Alvaro Fernandez have moved on loan to Nottingham Forest and Preston respectively.