The north Londoners have moved to sign the midfielder from Montpellier after being frustrated with their attempts to sign Morgan Schneiderlin from Southampton
The 24-year-old underwent a medical and formalised 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." - with Spurs following suit soon after.
Stambouli becomes the club's sixth signing of the summer, following the acquisitions of Michel Vorm, Eric Dier, Ben Davies, DeAndre Yedlin and Federico Fazio.
The arrival of Stambouli, a tough-tackling defensive midfielder, is expected signal the end of Spurs' pursuit of Southampton's Morgan Schneiderlin.
Pochettino was interested in securing the services of the Saints star and was prepared to make him his most expensive arrival this summer, but manager Ronald Koeman has been vocal in his reluctance to sell.
The Montpellier man has made 14 appearances for the France Under-21 side, though he has yet to earn a call-up to the senior national team.