Huerzeler replaces Roberto De Zerbi who left at the end of the league season having helped them qualify for European competition for the first time during his spell in charge.
The American-born coach guided St Pauli to the top of the second-tier in Germany, earning promotion to the Bundesliga as champions.
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 and 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."
Brighton finished 11th in the league last season after a gruelling campaign where they also reached the last 16 of the Europa League.
"The club has made incredible progress over the last few seasons and the aim is to continue building on that success," Huerzeler said. "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."
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