The Seagulls are understood to have paid approximately £11 million for a player who spent the past two seasons in Greece establishing himself as a consistent figure both domestically and in European competition.
Costinha made 74 appearances for Olympiacos after joining from Rio Ave in 2024, including seven Champions League matches this past season.
Fabian Hurzeler moved to secure a specialist right-back to cover the void left by Joel Veltman, who is out of contract at Brighton this summer, and to allow midfielder Mats Wieffer to operate in a more central role.
Brighton manager 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. He is also comfortable in and out of possession and will add competition at right-back."
Costinha described himself as a player who relishes the physical demands of the role.
"I fight for every duel," he said.
"I'm fast, I'm stronger. I like to run, to help. I like to fight for a title. It motivates a lot for this."
Born in Povoa de Varzim, Portugal, Costinha came through the academies at Porto and Braga before joining Rio Ave, where he made 121 first-team appearances and was named in the Primeira Liga Team of the Year for the 2023-24 season following five goals and six assists in all competitions.
His performances at Rio Ave attracted Olympiacos, who signed him for around £1.4 million in 2024, making the deal a substantial profit on their original outlay.
Costinha has represented Portugal at youth level from Under-18 through to Under-21.
Brighton qualified for Conference League football next season after finishing seventh in the Premier League, and Hurzeler is understood to see Costinha's European experience with Olympiacos as a significant factor in the recruitment decision.
The signing follows a pattern of Brighton targeting players who have proven themselves in major European competitions before arriving in England, giving Hurzeler a squad capable of managing the additional demands of a long domestic and continental season.