Clarke enjoyed an outstanding spell in charge at Rugby Park after taking over in October 2017 and led the club to third place in the Ladbrokes Premiership in 2018/19, securing a return to European football in the process.
He told the Killie website: "It has truly been an honour and privilege to work for Kilmarnock Football Club and I will always treasure the moments and memories created here.
“I’m extremely proud of all our achievements during my time in charge and I’m especially pleased that I was able to play a part in putting a smile back on the faces of Killie supporters."
Director Billy Bowie added: “Steve leaves an incredible legacy - delivering our best campaign in over half a century and providing European football for the first time since 2001.
"His place in this club’s illustrious history is assured and he will always be welcomed back to Rugby Park with open arms.”