The 26-year-old has put pen to paper on a five-year agreement and is scheduled to formally link up with the Premier League side at the beginning of July.
Costinha arrived at Olympiacos in July 2024 after an extended spell with Rio Ave, where he accumulated 121 senior appearances.
Since moving to Greece, he has added a further 74 outings across all competitions, establishing himself as a consistent presence in the squad.
On the international stage, he has represented Portugal national under-21 football team at youth level but is yet to earn a senior cap for Portugal.
Brighton head coach Fabian Hurzeler said: "Costinha is a player we have followed closely for some time.
"He has the defensive capabilities, intensity and understanding of what we value and we feel he will be an excellent addition to the squad.
"He is also comfortable in and out of possession of the ball and will add competition at right-back, alongside our existing options. I am delighted he has chosen to continue his development with us in the Premier League."