The Holland international will move to North London for £52 million.
Albion remain keen on bringing Croatia defender Niko Vuskovic in the opposite direction as the summer window gathers pace.
Tottenham had two earlier bids rejected for van Hecke, who had one year left on his Albion contract.
He will now link up again with his former Albion boss Roberto De Zerbi after the World Cup, in which he is starting for the Dutch alongside Virgil van Dijk.
Spurs have conceded 122 goals across the last two Premier League campaigns and De Zerbi has immediately got to work on bringing in defensive reinforcements with van Hecke’s addition following the arrivals of left-back Andy Robertson and centre-back Marcos Senesi.
But van Hecke will also offer a lot in terms of build-up play.
His departure had looked increasingly likely as last season wore on and Albion fans will now turn their attention to who comes in as a defensive recruit.