As recently as last Friday, it looked as though the retailer could be in line for a seemingly unlikely rescue, with a consortium led by retailer Greg Tufnell and backed by Portuguese investors reported to be close to a deal.
But the financial backing for that bid failed to materialise, sources told the BBC.
Other bidders included a consortium led by Matalan founder John Hargreaves and offers from Sports Direct's Mike Ashley and Poundstretcher boss Aziz Tayub. But administrators Duff & Phelps said that none of these had been acceptable, and as a result, ordered the wind down of the company.
All 163 stores will now close and as many as 11,000 jobs will be lost.
"Despite the considerable efforts of the administrators and BHS senior management, it has not been possible to agree a sale of the business," said the administrators in a statement.
"Although multiple offers were received, none were able to complete a deal due to the working capital required to secure the future of the company.
"Our thoughts today are with the employees. We thank them for their professionalism and hard work. We would also like to thank the great British public for helping us in our efforts to save BHS resulting in several weeks of significant sales."