Head of Club Strategy Oleg Yarovinsky has also left his role at the KCOM Stadium.
Tigers Vice-Chairman Ehab Allam said: “Leonid has worked tirelessly in his role and has acted with complete honour and been a pleasure to work with. Unfortunately results have not improved as both parties would have hoped and therefore it was agreed for the relationship to come to an end.
“I would like to thank Leonid and Oleg for their efforts here and sincerely wish them well for the future.”
On his departure Slutsky said: “I would like to really thank everyone associated with Hull City from the players and staff to the owner and especially the fans. ??
“I am very proud to have been through this experience, it was challenging but a very exciting time for me. ??
“Hull City will always be a part of my heart and I wish the team all the very best for the future.” ??
The process to recruit a new Head Coach is underway.