Sainsbury's said the move will create a "multi-product, multi-channel" business with around 200 stores.
The deal will see Sainsbury's pay 0.321 new shares and 55p per share in cash to buy Argos, and will see Home Retail Group shareholders hold 12% of the combined business.
Sainsbury's said the deal should be completed in the third quarter of this year.
Chairman David Tyler said: "We are very pleased the board of Home Retail Group has recommended our offer for the acquisition of its business to its shareholders.
"The combined business will offer a multi-product, multi-channel proposition, with fast delivery networks, which we believe will be very attractive to customers and which will create value to both sets of shareholders."
Home Retail Group chairman John Coombe added: "Argos is both an icon of the British high street and also a leader in the digital transformation of UK retailing.
"We are pleased that Sainsbury's has recognised our progress and our potential with its recommended acquisition of Home Retail Group."