The French manager has left the Parkhead club after winning just two matches of his eight in charge of the club.
Assistants Kwame Ampadu, Jules Gueguen, and Maxime Chalier leave Celtic with Nancy.
Head of football operations Paul Tisdale has also departed the club, as confirmed in a statement on Monday afternoon.
A club statement confirmed: “Celtic Football Club today announces that it has decided to terminate the contract of manager Wilfried Nancy, with immediate effect.Â
“The Club thanks Wilfried for his efforts and wishes him and his family well for the future.
“Wilfried’s assistants, Kwame Ampadu, Jules Gueguen, and Maxime Chalier, will also be leaving the club and they take with them our good wishes.
“The Club can also confirm that Paul Tisdale has left his position as Head of Football Operations. We thank Paul for the contribution he has made in that role.
“A further update will be provided to supporters as soon as is practical.”