The Blues' playing legend has spent the last 11 years at the club's Academy and has overseen the development of a number of the young players who have either broken into the first team or are poised to do so in coming seasons.
In his most recent role, he led the U18s to a Dallas Cup triumph last year and a Premier Academy League title before that.
Those successes represented a personal triumph for Sheedy after he overcame bowel cancer.
The reasons for his apparent departure from Everton have not yet known although there have been rumours of changes at Finch Farm that could see the Academy restructured.
Under the existing relationship, Sheedy had been sharing head-coaching responsibilities of the U18s with Paul Tate and John Ebbrell.