Dutch outlet Voetbal International reported on Tuesday that Brighton and Spurs had agreed on a deal worth £52 million.
Van Hecke, who'll be reunited with former coach Roberto De Zerbi, had agreed on personal terms with the North London outfit several weeks ago.
A move for Van Hecke seemed inevitable after the Dutchman refused to extend his Brighton contract, which expires in 2027.
The centre-half desired a move last summer already, but was refused one by the East Sussex club.
The transfer makes Van Hecke the fifth-most expensive arrival in Spurs history, only behind Xavi Simons, Dominic Solanke, Mohammed Kudus, and Tanguy Ndombele.
At the same time, Van Hecke will become the sixth-most expensive Dutchman of all time.
Van Hecke, 26, joined Brighton in 2020 from Dutch side NAC Breda.
After spending seasons on loan with Heerenveen and Blackburn, Van Hecke was introduced into the Brighton team under Graham Potter and De Zerbi.
In his four full seasons with the Seagulls, Van Hecke has played 131 games across all competitions.
As a Brighton standout, Van Hecke made his senior Netherlands debut in 2024 and has amassed 14 caps so far.
Van Hecke, whose uncle Jan Poortvliet started in the 1978 World Cup final for the Netherlands, is a starter at the 2026 World Cup, which for him started with a 2-2 draw against Japan on June 14th.