The 29-year-old right-back was on Liverpool's books as an 18-year-old, making just one appearance in a Champions League qualifier, and becomes the sixth summer signing by Boro's Spanish manager Aitor Karanka.
Spanish goalkeeper Victor Valdes arrived from Manchester United on a two-year contract last week.
Defensive midfielder Marten De Roon, winger Viktor Fischer, defenders Bernardo Espinosa and Jordan McGhee have also been recruited by Middlesbrough, who won promotion from the Championship last season.
"He (Barragan) is a player we know a lot about and he is a good addition to the squad," Karanka told the club website (www.mfc.co.uk). "He is a good lad, and he has played a lot of games for Valencia.
"He knows this country as well because he was at Liverpool as a young player."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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