The US supermarket chain will focus on its mainstay grocery business and will use the proceeds from the sale to buy back shares and reduce debt.
It is revamping nearly 2,800 brick-and-mortar supermarkets, cutting prices, improving in-store technology and investing in online channels.
Kroger in October announced that it was looking to sell its convenience store arm, which includes Turkey Hill, Loaf 'N Jug, Kwik Shop, and Tom Thumb.
The business generated US$4bn in revenue in 2016 and sold 1.2 billion gallons of fuel.
EG Group will continue to operate the stores under their established names and plans to establish a North American headquarters in Cincinnati.
Shares dipped 1.65% to US$28.05 each ahead of the opening bell in the US.