The Seagulls had two bids for the 19-year-old turned down last month before finally reaching an agreement. The deal includes potential add-ons that could push the overall fee up to £50m.
Vuskovic will undergo a medical once Croatia's World Cup campaign has ended. Croatia face Portugal in a last-32 tie in the early hours of Friday morning UK time.
Born in Split, Vuskovic came through the academy at local club Hajduk.
He became the youngest player to feature in Croatia's top flight at just 16 years old, and went on to become his club's youngest goalscorer.
Vuskovic agreed a deal with Tottenham in September 2023 that saw him officially join the Premier League club in 2025. Although he is yet to make his competitive debut for Spurs, Vuskovic spent last season on loan at German club Hamburg, making 30 appearances and scoring six goals in the Bundesliga.
The defender is regarded as one of the most highly rated young centre-backs in Europe, and Brighton's willingness to break their transfer record reflects the reputation he has built despite his tender age.
Vuskovic's rapid rise from Hajduk's academy to the brink of a Premier League move illustrates the scale of interest he has attracted since his breakthrough at 16. His time in Germany proved a valuable stepping stone, with regular first-team football at Hamburg helping him adjust to senior football outside his homeland.
Tottenham's decision to sanction the sale, having only signed him permanently this year, suggests the financial terms on offer from Brighton were considered too significant to turn down.
The move will not be finalised until after Croatia's involvement in the World Cup comes to an end, meaning Vuskovic's focus remains on international duty for now. Brighton's pursuit of the defender comes after two earlier bids were knocked back, a sign of the Seagulls' determination to land their man despite the initial resistance.
A club-record outlay underlines how highly Brighton rate the teenager's potential, with the fee eclipsing anything previously spent by the south-coast club on an individual signing.
For Tottenham, sanctioning the sale represents a swift turnaround on a player they only signed permanently in 2025, though the size of the fee on offer appears to have proven decisive.
Vuskovic's development at Hajduk, where he broke through as a 16-year-old, set the platform for the interest that has followed him through his move to England and his loan spell in Germany.