Orlandi has penned a two-year contract with the Seagulls.
Brighton boss Gus Poyet is delighted to have drafted a proven performer into his squad and is backing Orlandi to be a big hit.
He told the club's official website: "Andrea provides us with versatility and creativity across the midfield. He can play as a typical winger, or more central in a No.10 role.
"He has played a lot of games in the Championship for Swansea, helping them win promotion to the Premier League, and he has played at the top level.
"Andrea is a creative player who likes to get forward and attack and he will give us a different attacking option in midfield."