The $3.60 per share cash offer represents a 65 percent premium to Roundy's Tuesday close of $2.18.
Roundy's shares rose to $3.58 in premarket trading on Wednesday. Kroger's shares were up 2 percent at $38.08.
The deal has an equity value of $177.8 million, based on Roundy's outstanding shares as of Aug. 3.
Milwaukee-based Roundy's operates supermarkets under the Pick 'n Save, Copps and Metro Market and Mariano's banners, primarily in the upper Midwest.
The deal will give Kroger 151 retail grocery stores and 101 pharmacies, giving it a total of 2,774 stores in 35 states.
Kroger plans to finance the transaction with debt, and refinance Roundy's existing debt of $646 million.
The grocer said it expects the deal to add slightly to earnings in the first year after closing, and sees costs savings of about $40 million over time.