Chorlton had led the Grecians' board since December 2009 but was facing a vote of no-confidence from the Supporters' Trust, who own the Sky Bet League Two club.
A statement on the club's official website read: "Mr Chorlton wishes Exeter City AFC well in the future.
"He says the Club has a professional Board of Directors, an outstanding manager, a very talented young team, and a group of hard working staff.
"He thanks them for their support and friendship over the last four and a half years and wishes the club and its dedicated supporters a very successful 2014/15 season."
In May earlier this year, the cash-strapped Exeter decided to take a £100,000 loan from the PFA in order to pay their players after a fall in attendance and ticket sales.
This resulted in the Grecians being put under a transfer embargo until the debt is repaid.