The Seagulls will pay a fixed £46 million for the 19-year-old centre-back, with £4 million in performance-related add-ons.
Vuskovic, who featured for Croatia at the World Cup, has penned a five-year contract until 2031.
Spurs have also secured a 20 per cent sell-on clause on any profit made in a potential future sale.
"Luka has enjoyed a fantastic start to his career - it's one we’ve followed closely," Brighton head coach Fabian Hurzeler said.
"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 the Premier League. We are confident that he will take this in his stride though."
Vuskovic signed for Tottenham from Hajduk Split in 2023 as a 16-year-old, costing around £12 million.
He officially joined the club in July 2025 and scored during a pre-season friendly against Reading.
The 19-year-old was loaned to Hamburg in search of regular first-team minutes and shone during his Bundesliga stint.
He was named in the Bundesliga Team of the Season and won the Goal of the Year award for an improvised scorpion kick.
Vuskovic has six caps for Croatia and became their youngest-ever World Cup player in the summer.