Debenhams has secured eight stores, BHS has bought 10 and Primark has agreed to buy six sites.
The stores will change over to their new owners as soon as is practically possible the administrators said, preferably before the end of March.
Joint administrator Andrew Pepper said: 'We are delighted to be able to announce the completion of deals for 24 stores, which will hopefully safeguard more than 2,000 jobs. The sites are typically the flagship store in the area, so it is also fantastic news for customers and nearby retailers that the stores are being taken by leading high street retailers. Completing these deals quickly was imperative, because timely sales have helped maximise the retained value in the business for the benefit of creditors.'
Debenhams chief executive Rob Templeman said that the eight stores bought from Allders would be incorporated into the retailer's plan to roll out 200 stores across UK and Ireland. He said: 'We intend to bring the full Debenhams offer, including our fast-growing Designers at Debenhams ranges, to these locations as quickly as possible and are pleased to welcome Allders staff to the group.'