He revealed in July that he was willing to sell the club, but always stated that he would remain at Vicarage Road until a new buyer could be found.
His departure continues the turmoil at the Hornets, which saw Elton John, who was critical of Simpson's regime, give up his position as life president and former manager Aidy Boothroyd part company with the club by mutual consent last month.
Simpson appointed Chelsea youth-team coach Brendan Rodgers as Boothroyd's replacement only a week before his resignation.
Rodgers began his managerial reign on Saturday with a 1-1 draw at home to bottom club Doncaster.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.