Kean, who was Chris Coleman's right-hand man at Fulham and Real Sociedad before joining him at the Ricoh Arena, still has 12 months to run on his contract.
Coleman said: "We have been together for six years and get on very well but we felt this was the right time for a change. It is totally amicable.
"Steve remains an employee of Coventry City but should other opportunities arise for him he will be free to take them. I am sure that will happen sooner rather than later."