The deal is thought to be worth less than£20 million, but will safeguard the future of the retailer, which has been seeking a buyer since Christmas, when it came close to breaking its banking covenants.
Adams has been circled by restructuring specialists including Hilco and Gordon Brothers since December. Some 100 of its 300 stores are believed to be unprofitable.
Shannon netted about£10 million when he sold his stake in Stead & Simpson last year.
Bridgepoint Capital and Lloyds Development Capital are expected to lose their equity in the business.
No comment was available from PricewaterhouseCoopers, which is selling the chain.