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."

Mark Jones, 45, of Cwmbran, denies murdering Amelia Jones in Pontnewydd in November, 2012.
His daughter Sarah Jones was asked by the defence barrister, Roger Thomas QC, about a trip to the doctors with Amelia on 7 November 2012.
She admitted "exaggerating" about the doctor's diagnosis.
Mr Thomas asked her what the diagnosis was and Ms Jones told the court: "She had a cold".
The court was told that she had previously said, in a text message: "They want to check her, and they might keep her in overnight".
Mr Thomas suggested those two accounts differed from each other.
Sarah Jones replied "Don't you over-exaggerate with stuff sometimes". Mr Thomas asked, "So you do exaggerate?"
Ms Jones then replied: "Yes".
Ms Jones, 26, told Newport Crown Court on Tuesday she found Amelia in tears after leaving her in Mr Jones's care in a car during a shopping trip, days before her death.
The defendant's barrister quizzed Ms Jones as to why she gave uncertain answers in a police interview about whether she actually went shopping on that day.
She said from the stand: "I had all my other children taken off me, I had been arrested for murder; I wasn't in the right frame of mind."
Ms Jones was later released and her children were returned to her, the court heard.
But Mr Thomas said the incident relating to Amelia being upset in Mr Jones's care "didn't happen at all like this".
He said "Amelia was left alone in the house with Mark", and not in a car, as she had suggested.
The QC accused Ms Jones of "not being entirely fair and truthful" about her recollection, adding: "The incident you have described yesterday did not occur".
"It did occur", she replied.
Prosecuting counsel, Paul Lewis, asked Ms Jones if she had "ever laid a finger on Amelia, so as to harm her".
She replied: "No, not at all".
Ms Jones told the court she now has another child with Amelia's father, Ian Skillern, who was born in 2013.
The pair are no longer in a relationship.
During earlier evidence, Ms Jones claimed her father said Amelia had been "a nightmare" when he babysat the night before the baby received her fatal injuries.
Mr Jones insists he dropped Amelia accidentally on the two separate evenings while babysitting on his own.
The case continues.
Aston Villa chief executive Tom Fox has stepped down with immediate effect.
[NEXT_CONCEPT]
The mother of a baby girl allegedly murdered by her own grandfather has admitted she "exaggerates", a court has heard.