Owner Randy Lerner, who put the club up for sale in May, is said to have flown into Birmingham from the USA this week to convince Fox to leave his role at the Emirates.
"I was delighted and even flattered by Tom's interest in the Villa job," the club's Twitter page quotes Lerner as saying. "Tom's achievements at Arsenal speak for themselves. Tom's reputation as a leader and team builder makes him, to my mind, a great fit to take our club forward."
Fox added: "The chance to work with Randy, Paul Lambert and Robin to help restore Aston Villa to its rightful place in the Premier League is a challenge I'm really energised by and greatly looking forward to."
American Fox, who spent five years at Arsenal, will replace Paul Faulkner, who left his role at the Midlands club last month.