A deal was struck over the weekend and the defensive midfielder has now signed on after passing a medical in north London.
Stambouli was linked with Swansea and Fiorentina earlier in the summer but instead becomess Mauricio Pochettino's sixth major signing at Spurs.
He said: "I'm very happy to be here. I'm discovering the Training Centre. It's amazing to be here and I am determined to show people I can play.
"I know the size of the club and I am happy and proud to join. I will give everything for the club."
Montpellier coach Rolland Courbis has wished the 24-year-old well, saying: "Signing for Tottenham is a great step forward.
"He should be able to join the French team. Tottenham had a very good idea to sign him."
Stambouli's arrival could coincide with the departure of Sandro, who is wanted by QPR, while Lewis Holtby has left White Hart Lane to join Hamburg on loan.