The owner of Poundland has agreed to take on the leases of dozens of Wilko shops.
Pepco Group, which owns Poundland in the UK, is expected to convert up to 71 Wilko stores to the Poundland brand.
Poundland boss Barry Williams said it recognised the last few weeks had been difficult for Wilko workers.
In a statement, the company said that Wilko staff would have priority when applying for new jobs at the Poundland shops.
Wilko fell into administration in August as it struggled with sharp losses and a cash shortage.
It was founded in 1930 and by the 1990s became one of Britain's fastest-growing retailers.
But the discount chain has faced strong competition from competitors including B&M, Poundland and Home Bargains, as the high cost of living has pushed shoppers to seek out bargains.
The first Wilko shop closures are taking place on Tuesday after administrators PwC failed to find a buyer for the bulk of the business.
Mr Williams, the managing director of Poundland, said the company would work quickly with landlords in the coming weeks to get its new shops open once the administration process is wound up.
It said that the announcement would mark some "positive news for customers and those High Streets that faced the loss of an important retailer".
In an interview with the BBC, Mr Williams insisted that there is "plenty of life" left on the High Street but it was down to discount retailers to "stay close" to customers and ensure that their offer matches up with what customers need.
Many Wilko shops are in High Street locations in traditional town centres. While these locations are convenient for shoppers without cars, since the pandemic there has been a shift to bigger retail parks and out-of-town options with more space, benefiting other shops.
Independent retail analyst Maureen Hinton said Wilko's store locations were part of its problems.
"Accessibility for the kind of products it was selling is very limited - it's very difficult to carry home bulky products from a High Street where you can't have access to cars and parking, which is being deterred in High Streets," she told the BBC.
Rival B&M has also agreed to buy 51 of Wilko's buildings in a £13m deal, but it is understood the stores will not be run under the Wilko brand.
The 71 shops included in the deal with Pepco and the 51 stores taken on by B&M currently employ about 3,200 Wilko workers.
In a statement, the Poundland owner said that it expected the rebranded shops to open by the end of this year, although workers will not be transferred directly.
Poundland has undergone a big transformation in recent years, adding chilled and frozen food as well as clothes to its offer.
The deal will see the Wilko sites added to its 800 existing shops in the UK.
Mr Williams added: "What's happened with Wilko is really a sad situation indeed... Don't confuse that though with the state of the High Street. We're thriving and we're growing and this is an opportunity to demonstrate that - and that gives a home to some of these Wilko colleagues."
Which Wilko stores are Poundland taking on?
The 71 store locations are:
Aberdare, Alfreton, Alnwick, Altrincham, Ammanford, Ashby, Barking, Bedminster, Beeston, Bicester, Bishop Stortford, Bletchley, Bolton, Brentwood, Brigg, Cambridge, Chepstow, Coalville, Cramlington, Droitwich, Eccles, Edmonton Green, Ellesmere Port, Ferndown, Gateshead, Grays, Greenock, Grimsby, Havant, Hayes, Headingley, Hessle Road - Hull, Hillsborough, Hitchin, Jarrow, Killingworth, Kimberley, Lee Circle, Leek, Leigh, Lichfield, Maidenhead, Matlock, Melton Mowbray, Nelson, Northallerton, Orton, Pembroke Dock, Peterlee, Pontefract, Pontypool, Redhill, Redruth, Ripley, Rugeley, Sale, Seaham, Selly Oak, Shrewsbury Darwin Centre, South Shields, Southport, Stafford, Stamford, Stockport, Thornaby, Wellington, Wembley, West Ealing, Wombwell, Worcester and Worksop, where Wilko's head office is located.
Earlier this week, Wilko's administrators said the group's remaining workers in its shops, warehouse and support centres were set to lose their jobs after a rescue bid by Canadian entrepreneur Doug Putman failed.
The billionaire owner of music retailer HMV had been trying to buy at least 100 Wilko shops but the deal fell through as rising costs complicated the deal.
Administrators said that they were confident the Poundland deal would "create a platform for future employment opportunities" for Wilko employees.
Edward Williams, joint administrator at PwC, said: "We will continue to engage with other retailers around any interest in other Wilko sites and are confident of completing a sale of the brand and intellectual property within the coming days."
Several other retailers and investors have reportedly been in talks with PwC about potentially buying the Wilko brand and website.
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