The Albion centre-back passed a medical while with the Holland squad at the World Cup.
He has agreed what Spurs have called a long-term deal.
Seagulls head coach Fabian Hurzeler said: “JP has been a pleasure to work with during our two years together and I wish him well in this move to Tottenham.
“He has been a huge influence on and off the pitch, endearing himself to both fans and his team-mates with his commitment. I have no doubt he will continue to be a success.”
Albion have secured a 20% cut of any future profit Spurs receive for the Holland international.
Van Hecke links up with his former Albion boss Roberto De Zerbi, who took over at Spurs towards the end of last season.
The defender said: "I already have a really strong connection with the head coach, who I'm looking forward to working with again.
“Micky (van de Ven, Holland defender) 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."