Fox was the right-hand man of the club's U.S. owner Randy Lerner, who put Villa up for sale last May but has yet to find a buyer.
Seven-times champions Villa are last in the 20-team league, eight points behind 19th-placed Newcastle United and nine from safety.
"Regarding my resignation, 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," Fox said.
"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."
The club's German sporting director Hendrik Almstadt left on Tuesday and manager Remi Garde's future has been the subject of media speculation, with reports linking him to a return to Ligue 1 club Lyon.
The Frenchman, who replaced Tim Sherwood in November, described Villa's plight on Thursday as "an impossible mission that we have to make possible" and said he was fully focused on the task.
Fox joined in 2014 from Arsenal, where he had worked with Almstadt and been chief commercial officer, and has incurred the wrath of fans who have protested against Lerner at recent matches.
Lerner appointed Steve Hollis as chairman in January, signalling his intention to take a step back from the running of the club.
Villa said Hollis would become executive chairman until a permanent replacement for Fox was found.
(Reporting by Alan Baldwin, editing by Ossian Shine and Clare Fallon)
Share
