The 31-year-old, the youngest full-time manager in Premier League history, has taken over at the south coast club after guiding St Pauli to promotion into Germany's elite Bundesliga last season.
The Texas-born German coach said he had moved to "the best league in the world" ahead of Brighton's opening league fixture of the 2024/25 season at Everton on August 17.
"I'm aware this is a huge job. It's a big challenge and I think I need a lot of courage and ability so I need to stay humble," said Hurzeler.
"My targets, I want to discuss them with my players, they need to be convinced of that, they need to feel what we can achieve, that's the main thing for me.
"I want to achieve big things and I want to challenge the establishment.
"The Premier League is the best league in the world with a lot of good coaches. You need your own philosophy and identity but it's important to take other elements and adapt."
Hurzeler, who has signed a contract with Brighton until 2027, has replaced Roberto De Zerbi at the Amex Stadium after the Italian left at the end of last term after two successful seasons in charge before taking over at French club Marseille.
De Zerbi took charge at the Amex Stadium in September 2022 and led Brighton to their highest ever top-flight finish when they came sixth in 2022/23.
'Least risk option'
It meant the Seagulls competed in European football for the first time in their history, advancing to the Europa League last 16 before losing to Roma 4-1 on aggregate.
But the Seagulls struggled to replicate that fine domestic form during an injury-plagued 2023/24 season that ended with a mid-table finish in the Premier League.
Hurzeler added: "Roberto De Zerbi had a huge impact on the football world with a different style of football. Of course I will take some elements (from him) but I have my own philosophy and you can't copy anyone.
"I like the football he played, it had a lot of courage with some interesting elements which I will also try and adapt to my philosophy."
Brighton chairman Tony Bloom, a professional gambler, insisted he had not taken a punt on hiring Hurezeler despite his new recruit's limited experience as a head coach.
"The whole city should be very excited," said Bloom. "I wouldn't talk about it as a gamble at all.
"We look at everything, we put a lot of effort into the appointment of any head coach like other clubs do and we think Fabian is the best fit for the football club. He's the least risk option we had."
