The Netherlands international, 26, has signed a long-term contract and will reunite with old boss Roberto de Zerbi in North London.
He is Spurs' third signing of the summer after the free acquisitions of left-back Andy Robertson and centre-back Marcos Senesi.
A Brighton exit for Van Hecke appeared inevitable after it became clear he would not extend his contract, which was due to end in 12 months.
"It's a huge honour to become a Spurs player and when you join such a big club, it's a dream come true," Van Hecke told the club's official website.
"I already have a really strong connection with the Head Coach, who I'm looking forward to working with again. Micky (van de Ven) has also told me some great things about the Club, so I can't wait to get started.
"I've been at Tottenham Hotspur Stadium as an opposition player and now I'm looking forward to walking out there in front of our fans wearing the Spurs shirt. That will be a special moment."
Van Hecke joined Brighton from Dutch side NAC Breda in 2020, but only emerged in the first team two years later.
He started 36 Premier League games in the recent season as he helped the Seagulls qualify for the Conference League.
Van Hecke made 131 appearances in total for the East Sussex club.
Van Hecke is currently at the World Cup representing the Netherlands alongside fellow Spurs defender Micky van de Ven.
Brighton, meanwhile, retain an interest in 19-year-old Spurs centre-back Luka Vuskovic as a potential replacement.
They have seen two bids for the Croatian prospect rejected, with the latest reportedly worth £35 million.
