Argos, which is part of the GUS catalogue shopping empire, will rebrand the 33 stores and around 800 staff will transfer over as part of the £444m deal.
According to reports, most of the stores being closed by Sir David and Sir Frederick Barclay trade within Littlewoods stores, which are also owned by the billionaire brothers.
Littlewoods had already branded those Index operations as Littlewoods Extra.
Index is being closed after racking up losses of over £100m over the last 20 years, according to its chairman David Simons.
"Index has made a loss in nearly every year of its 20-year history despite many attempts by different management teams to turn the business around. The decision to divest the business has not been an easy one to make, but it is the only solution to a difficult and unsustainable situation," Simons said.
He added: "Our concern now is for those employees affected and we will work hard with them and the unions to achieve the best outcome we can."
Closure of the Index brand will increase speculation that Littlewoods chain, which comprises 119 stores, will be next to be sold off.
Earlier this year, Wal-Mart-owned Asda bid as much as £500m for the chain. Other possible bidders could include discount fashion chains Primark and and New Look.
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