The decision to ship him out of north London comes a year after the Dutch forward joined Tottenham from AZ Alkmaar.
Janssen was offered a chance to remain in England, but rejected an opportunity to join Brighton & Hove Albion on loan last week, according to David Hynter of the Guardian.
He becomes the second Tottenham flop to join the Turkish side after Roberto Soldado joined Fenerbahce last month. Former Arsenal and Manchester United striker Robin van Persie joined Fenerbahce in 2016.
He led all Eredivisie scorers in his final season before moving to the Premier League, where he only managed to score six goals in 39 appearances.