O'Riley agreed on a five-year contract with the Premier League club and will move to the Amex Stadium subject to international clearance.
The Denmark international featured more than 100 times for the Hoops after arriving from Milton Keynes Dons in 2022, scoring 27 goals and helping Celtic win the Scottish Premiership three times.
He hit 19 goals and also contributed 18 assists during Celtic's title-winning campaign last term.
Celtic had rejected several offers for O'Riley from Europa League holders Atalanta and Spanish club Atletico Madrid before finally accepting Brighton's bid.
Brighton boss Fabian Hurzeler said: "He plays a very specialist position. He is very good at occupying and attacking the right space and likes making deep runs, knowing when to attack at the right time.
"He enjoys getting forward and attacking the opponent's penalty area, but he also has a good defensive instinct. That balance makes him special.
"He is a great character, and has a good ambition to succeed and that's something which is very important for us."