All Netto branches will be converted to Asda fascias and be integrated into its supermarkets division for shops of under 25,000 sq ft.
Asda said it expected the deal to be completed this summer and for stores to be converted to the Asda format by the middle of next year.
Netto was founded in the UK in 1990 and has 193 branches with an average sales area of 8,000 sq ft.
Claus Juel-Jensen, managing director of Netto, said Asda was “the ideal purchaser of our UK business”.
Netto will focus its energies on growth in Scandinavia, Germany and Poland.
Asda chef executive Andy Clarke said: “Customers will benefit from low prices on a significantly broader range of quality products, complemented by the wide range of services we offer in our smaller stores.”