Spurs will pay around €11m for the winger, who looked set to join the north London club a numbr of weeks ago.
However, Tottenham chairman Daniel Levy wanted to restructure payments which included paying a smaller up-front sum, something which Marseille were not prepared to accept.
The deal will also see striker Clinton Njie move to Marseille on a season-long loan after the Cameroonian endured a disappointing first season at White Hart Lane.
Nkoudou played 41 games for Marseille last season, scoring 10 goals.