Kluitenberg, 54, first linked up with Koeman at AZ Alkmaar in 2009, before following the former Valencia manager to Feyenoord, Southampton and then Goodison Park.
The outspoken fitness coach was one of Koeman's most trusted staff members on Merseyside, but the Liverpool Echo reported back in September that he had deactivated his Twitter account following claims the Toffees squad was unfit.
The Dutchman posted his first tweet since deactivating his account two months ago, stating it "was a pleasure" to work for Everton after first joining the Merseyside club in June 2016.
I like to thank the board, the directors, the whole staff, the players and all fans! Was a pleasure to work for @Everton Football Club. Wish you all the best for the future.— Jan Kluitenberg (@jankluit) November 16, 2017
Kluitenberg leaves Everton ahead of the Toffees clash against Crystal Palace, as they travel to Selhurst Park to take on Roy Hodgson's side on Saturday afternoon.
Interim manager David Unsworth will be looking to further strengthen his claims for the permanent role with a second win in charge, after beating Watford 3-2 last time out following three successive defeats to Chelsea, Leicester City and Lyon.
Three points for the Toffees could see them climb the Premier League table even further into 12th place, if Stoke City, Southampton and Leicester drop points.