Borders, which has 45 stores in the UK, had remained opened for trading
The Borders bookshop chain will close all its branches in the UK next week.
The chain went into administration earlier this month and had kept open all its stores while it attempted to find a buyer.
Administrators MCR said all 45 Borders and Books Etc stores would close on 22 December.
Borders has suffered from increased competition from online retailers and supermarkets. Borders employed 1,150 people in total.
"The joint administrators have been pursuing a sale of the business," MCR said.
"However, it has not been possible to agree a sale of any part of the business as a going concern."
The Borders chain was originally owned by the US book giant of the same name, but was sold in June 2007 to Risk Capital Partners, which is headed by Channel 4 chairman Luke Johnson.
Risk Capital then sold it on to the private equity firm Valco earlier this year.
MCR has previously said Borders had "severe cash flow pressures" and that several suppliers had stopped or reduced its credit, which made suppliers less willing to trade with the retailer and made it difficult for it to replenish its stock levels.