The Range has agreed a deal to buy the Wilko brand after a rescue bid for the wider business fell through.
The agreement means it will own Wilko's website and could choose to stock and sell some of its products.
Administrators said 36 Wilko workers had transferred over to The Range and it expects the online operations to restart in early October.
However, the deal, understood to be worth £5m, will not prevent Wilko shops disappearing from UK High Streets.
Nearly all of the company's 12,500 staff will lose their jobs as a result of the closures.
Wilko's rivals have been snapping up parts of the company since administrators were unable to find a buyer for the whole business.
Some staff may be re-employed as a result.
Jane Steer, one of the PwC administrators, said Wilko "remains a much loved and trusted brand within the UK", adding that deal with The Range means "the Wilko name lives on".
The Range, which has 210 UK stores, also plans to sell click-and-collect products from the Wilko.com website.
Its chief executive, Alex Simpkin, said The Range was delighted to have bought the Wilko brand, which "comes at a time when consumers are more than ever wanting to shop with confidence for value and quality".
Wilko is known as a value-led store, and consumers have increasingly been looking for bargains during the cost of living crisis.
But the company, founded in 1930 and a stalwart of High Streets up and down the country, fell into administration in August as it struggled with sharp losses and a cash shortage.
The billionaire owner of HMV, Doug Putman, initially hoped to keep as many as 300 Wilko shops open, but his bid failed and no other bidders were interested in running the shops under the Wilko name.
On Tuesday, the owner of Poundland agreed a deal to take on the leases of about 71 Wilko shops, which will reopen under its own brand.
Another rival B&M has also agreed to buy 51 of Wilko's shops in a £13m deal.
Which Wilko stores are closing on Thursday?
The first Wilko shops to cease trading shut on Tuesday. A further 28 will close on Thursday:
Barrow in Furness
Queen Street Cardiff