The North Londoners have moved to sign the midfielder from Montpellier, with the 24-year-old having previously been linked with a move to Swansea.
The 24-year-old underwent a medical and formalized his move to White Hart Lane on transfer deadline day, with the former France Under-21 international signing a five-year deal.
Montpeiller present Louis Nicollin confirmed the move earlier in the day, telling reporters: "Stambouli to Tottenham, it's official." Spurs followed suit soon after, announcing the news on Twitter.
Stambouli had also been linked with Swansea but the North Londoners moved to beat out their Premier League rivals earlier this week. He becomes the club's sixth signing of the summer, following the acquisitions of Michel Vorm, Eric Dier, Ben Davies, DeAndre Yedlin and Federico Fazio.