Stambouli is believed to have put pen to paper on a five-year deal at White Hart Lane, becoming Tottenham's fifth signing of the transfer window.
The 24-year-old has established himself as one of the best midfielders in the French top flight and has long been linked with a move away from the Stade de la Mosson.
Swansea City and Fiorentina were also rumoured to be interested in Stambouli's services, but it is Mauricio Pochettino who has won the race for his signature.
Marseille-born Stambouli emerged through the youth ranks at Montpellier and was part of the side that beat big-spending Paris Saint-Germain to the Ligue 1 title in 2011-12.
Now he will look to further his reputation in the Premier League, with his arrival boosting a Tottenham side that lost 3-0 against Liverpool on Sunday.
The former France Under-21 international made 129 appearances in his career at Montpellier, scoring four goals.
