Jones, who was knighted in yesterday's New Year's Honours list, swaps roles with current chairman Roger Lane-Smith, who becomes non-executive deputy chairman. Chris Ronnie remains chief executive.
Jones is best known as former chief executive of Next, and has also served on the boards of Morrisons and Littlewoods-owner Shop Direct Group.
At the same time, JJB has appointed former Selfridges chief executive Williams to the board as an executive director with particular responsibility for the company's strategic development. He will report to Jones and starts his new role on Monday.
"We are facing the most difficult retail environment I have ever experienced," said Jones, "but I am looking forward to working with Chris and Peter to re-establish JJB as a major force in the sportswear market."