PRWeek understands the split to be amicable and that he will remain in the role until next year.
The news follows the sudden departure, two weeks ago, of Chelsea chief executive Peter Kenyon.
Greenberg, a former sports editor of the Evening Standard and head of sport at News of the World, joined Chelsea in 2004.
He has regularly found himself in the eye of the media storm, having worked closely with tempestuous coach Jose Mourinho and through a series of managerial appointments and scandals.
Well-networked and well-known, another high profile management role in sport seems only a matter of time.
Chelsea Football Club comms chief Simon Greenberg resigns
PRWeek can reveal that Simon Greenberg, Chelsea Football Club's high profile communications and public affairs director, resigned yesterday without another role lined up.
