ICA-handlarnas Forbund's and AMF's joint bidding company Murgrona Holding said in a statement they were offering other owners 534 crowns per share.
The offer represents an 11% premium to the closing price for ICA Gruppen's shares on Nov. 9.
ICA-handlarnas Forbund, which currently holds 54% of ICA Gruppen and is an association of ICA store owners, would after the deal hold 87% of shares in Murgrona Holding and AMF 13%.
"ICA Gruppen in an unlisted environment, enables a more long-term investment horizon and a growth enhancing focus and is thus considered to be most favourable to carry out the changes that ICA-handlarnas Forbund deems necessary," they said.
ICA Gruppen's shares have been rising since late October when a media report pointed to the company as an attractive buyout candidate.
Murgrona Holding noted that the offer represented a premium of 29% compared to before the market speculation regarding a potential public offer that followed on the media report.
ICA Gruppen said in a separate statement its board unanimously recommended shareholders to accept the offer.
Swedish grocery store chain ICA Sverige accounts for the bulk of ICA Gruppen's business. ICA Gruppen also owns a pharmacy chain, a grocery retain chain in the Baltics, and a bank.
ICA Gruppen's shares stood at 533 crowns in early trade.
($1 = 8.5743 Swedish crowns)
(This story corrects to Wednesday in paragraph 1 and Nov. 9 in paragraph 3)
(Reporting by Anna Ringstrom; editing by Niklas Pollard)