He worked closely with owner Randy Lerner, who put the club up for sale last May but is yet to find a buyer.
The resignation of American Fox after 18 months at the Premier League's bottom club follows the departure of sporting director Hendrik Almstadt and three new appointments to the board.
Fox said "it makes sense for me to seek another challenge" following the changes in the Villa boardroom.
Villa are nine points from safety at the foot of the league and Fox and Lerner have been the target of fans' anger over their struggles.
Steven Hollis became the club's new chairman in January while former Governor of the Bank of England Lord King and ex-Football Association chairman David Bernstein have become directors at Villa Park.
And Gulf War commander General Charles Krulak is now listed as a director on the Companies House website.
In a statement Fox said: "The owner made it very clear last summer that he and I would seek to recruit a board that would put the club in a stronger position in the event that a sale didn't happen.
"As the board has taken shape, however, it has become clear that my role also has changed. While I am supportive of where the board is trying to take the club, it is my feeling that given the changes they are making, it makes sense for me to seek another challenge."
Aston Villa chief executive Tom Fox has stepped down with immediate effect.