The 50-year-old will lead the Blues' attempt to expand their brand around the world as they seek to become a growing force on and off the field.
"The club believes Mr Purslow has the vision and the leadership qualities to help us achieve these plans," said a short statement on Chelsea's website.
Purslow joined Liverpool in June 2009, succeeding Rick Parry, with the aim of bringing more revenue to the club although his role changed when then owners George Gillett and Tom Hicks decided to sell the club
The businessman then helped the sale process to the group led by current Reds owner John W Henry before stepping down from his role in October the following year.
He remained as a non-executive director and special adviser until February 2011.
Purslow fills part of the void created when Ron Gourlay left his role last week after five years as chief executive
Gourlay's non-commercial activities will be assumed by Chelsea chairman Bruce Buck and director Marina Granovskaia, who are both members of the club's board.
Source : PA