The 27-year-old right-back, who is a product of Barcelona's academy, has signed a four-year contract with Albion, which is subject to an international clearance.
Seagulls boss 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."