The high-street chain fell into administration last month and was forced to close its near-200 stores across the UK at a loss of 1,400 jobs, after being hit by increased competition from internet retailers and supermarkets.
Administrator PricewaterHouseCoopers (PwC) has announced that the Jessops "brand and other assets" have been acquired a group led by Jones. The consortium is understood to have faced competition from retail restructuring firm Hilco, which is interested in acquiring HMV.
However, Jones has not purchased Jessops' retail stores, with a buyer for those yet to be found.
A PwC spokesman said: "We can confirm we have sold the brand and certain other assets to a number of buyers, including entrepreneur Peter Jones CBE."