The Croatia defender has joined from Spurs for an undisclosed fee believed to exceed the £40 million the Seagulls paid Leeds for Georginio Rutter almost two years ago.
He has committed to a five-year contract with the option of a further year and will look to build on an impressive season on loan at Hamburger SV in Germany last term.
As the transfer was announced, Albion head coach Fabian Hurzeler said: “Luka has enjoyed a fantastic start to his career - it’s one we’ve followed closely.
“Last season he demonstrated he can play at a very high level and we want to help him build on that within our environment.
“There’s been a lot of external noise about Luka joining us, but he is still a young guy who will need time to adjust to the demands of playing for Brighton and to the Premier League.
“We are confident that he will take this in his stride though.”
Vuskovic started against England in the opening World Cup match but was then on the bench in subsequent fixtures as his side switched from a back three to a four.
There was known to be widespread interest in his services, notably from Barcelona.
Albion have described him as as “one of the most sought after young defenders on the continent”.
Vuskovic, 19, was named in the Bundesliga team of the season and also has an eye for goal.
He is the third centre-back to join the club this summer following Martin Svoboda from Venezia and Pascal Struijk from Leeds.