Just 31, Hürzeler leaves St Pauli after guiding them to promotion to the Bundeslisga.
He has agreed a contract until June 2027.
Brighton chairman Tony Bloom said, “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 eighteen months.
“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.”
Deputy chairman and chief executive Paul Barber added, “Away from the pressure of the regular season, we have taken our time to get this appointment right and are delighted to have agreed with Fabian to become our new head coach.
“He has already shown in a relatively short space of time as a head coach that he is one of the most innovative coaches working in football, and we are looking forward to getting ready for next season.”
Technical director David Weir added, “We will work closely with Fabian to help him settle in, and to get to know the club, staff and the area.
“Fabian already has an excellent knowledge of our squad and players, and we will be working to strengthen an already very strong squad during the transfer window.
“We will confirm all of Fabian's immediate backroom staff in due course, although Andrew Crofts and Jack Stern will be part of that coaching group, as first-team coach and goalkeeping coach respectively.”