Hurzeler, who helped St Pauli to promotion to the Bundesliga, has signed a three-year contract until 2027.
"I am absolutely thrilled to be the new head coach of Brighton & Hove Albion," Hurzeler told the club's official channels.
"After speaking to Tony (Bloom), Paul (Barber) and David (Weir), it was clear that they are highly ambitious. The club has a unique history and bold vision for the future, so I am truly excited to be part of the project.
"The club has made incredible progress over the last few seasons and the aim is to continue building on that success. I am relishing the opportunity to coach in the Premier League, and I can't wait to meet the players, staff and, of course, the fans."
Hurzeler, who succeeds Roberto De Zerbi at the helm, will begin to work with his new side for pre-season after receiving his work permit.
Brighton chairman Bloom said the German was the "standout candidate" in his manager search at the season's end.
"From the start of the process to appoint our new head coach, Fabian was always a standout candidate and one who had caught our attention with his exceptional work at St Pauli over the past 18 months," Bloom said.
"He has a style of play that aligns with how we want a Brighton & Hove Albion team to play, and I'm confident it is one our supporters will appreciate and enjoy.
"Fabian also has an excellent coaching pedigree and has worked with the German federation at various age group levels. We are really excited to start working with Fabian to prepare for the upcoming season."