The former Barcelona and Inter Milan defender has joined on undisclosed terms, with the move subject to international clearance.
Albion submitted a deal sheet to the Premier League - allowing the club an additional two hours to provide the remaining documentation on the transfer - and completed the deal ahead of the 7pm deadline.
Montoya spent nine years in the academy at Barcelona, before graduating to the club’s B side in 2009. He broke into the senior Barcelona side in 2011 and made 67 appearances, helping the club to seven trophies - including one Champions League win and three La Liga titles.
He spent the 2015/16 season on loan at Inter Milan and Real Betis, before moving to Valencia in 2016 where he made more than 50 appearances - and also played alongside Albion goalkeeper Mathew Ryan.
Seagulls manager Chris Hughton said: “Martin’s pedigree is excellent, and I’m delighted we have been able to add a player of his standing to our squad. There is no doubt he will improve our options in the right-back position.
“He’s won several domestic and European honours in Spain, and played the majority of his career in the top level of La Liga. He has a wealth of experience, at 27 years old he is a very good age, and I’m now looking forward to working with him.”