Villa say the 54-year-old will "take over the day-to-day running of the club with immediate effect" and will replace the suspended Keith Wyness.
The West Midlands outfit had been having financial trouble over the summer but billionaire businessmen Wes Edens and Nassef Sawiris bought a stake in the club, with owner Dr Tony Xia becoming co-chairman.
Dr Xia believes that Purslow's appointment represents a big step forward for the club and is looking forward to have him on board.
"I am delighted to welcome Christian, who will work closely with Nassef, Wes and myself to move the club in a better direction. I look forward to seeing him shine at our football club," Dr Xia said in a statement.
"This is an important step on our journey to return Aston Villa back to the elite of English football," added Sawiris and Edens.