The news brings an end to speculation as to who would buy the ailing retailer, with Marketing reporting on Monday (9 March) that Green was close to signing a deal.
In a statement Green said: "I am pleased that we have found a buyer in Retail Acquisitions Ltd who wants to develop the BHS brand. Having acquired the business nearly 15 years ago in May 2000, one of my clear objectives in identifying a purchaser was ensuring their desire to take the business forward."
Green bought the retailer in 2000, for £200m but the department chain has struggled, especially in the face of competition from budget clothing chains including Primark.
Green added: "BHS has a strong portfolio of 171 store sites throughout the UK, significant assets, long-standing and loyal suppliers and great international franchise partners. I am deeply proud of the work ethic displayed by the very many people I have worked with for so long at BHS, both within our Head Office and across the stores."
Simon Horner, head of fashion at research group Kantar Worldpanel, said that BHS has lost almost 800,000 shoppers in the past five years, and failed to stand up to growing competition from the likes of John Lewis, TK Maxx and Sainsbury’s.
He added: "BHS has not sufficiently capitalised on the growth of online retail and consequently only 9% of its fashion sales come from this channel versus 20% for the total market.
"BHS is still performing well among its traditional customers, those aged 55 and over. Over half of its sales come from this older demographic which accounts for nearly a third of all fashion spending in Britain.
"However, this age-group is choosing to follow younger fashion trends so BHS will need to refocus its offer to continue to appeal to these shoppers."
Retail Acquisitions has been set up by financier Keith Smith.