Mr 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 manager, who was born to a Jewish father in Volgograd in 1971, arrived on Humberside with a considerable footballing pedigree, having coached the Russian national team at Euro 2016 after winning three titles with CSKA Moscow.
Hull 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."
