Kwik Save fell into administration four years ago and stopped trading in 2009.
Costcutter subsequently trademarked the term "Kwik Save" and is now to launch Kwik Save-branded stores next year.
The roll-out of the Kwik Save brands forms part of Costcutter's strategy of segmenting its stores in order to appeal to all demographics. Kwik Save will be Costcutter's budget offering.
Costcutter marketing director Ian Bishop revealed to Marketing that the first two Kwik Saves will be in the north and south of England, but would not disclose their exact locations.
The convenience store brand, which operates as a franchise, has also created a top end brand called Mycostcutter and will give its core mid-market Costcutter brand a refresh as it attempts to move away from a "one size fits all" approach.
Bishop said: "We tried to do one size fits all and that is one of the biggest problems we had.
"With the greatest respect, there's no point putting a beautiful M&S store in a very dark and dingy council estate."
Costcutter's reprisal of the Kwik Save brand will stay true to the original values of budget supermarket Kwik Save, which ceased trading in 2009.
Bishop said: "It will be a little bit of 'pile it high, sell it cheap', which is what the Kwik Save brand was before, but in convenience format."
Costcutter's approach to tailoring its brands to the local community will be supported by a television campaign positioning the brand as the hub of the community, which will launch next year.
The 'Local Pride' television campaign will be created by Banana Kick and feature a caricature family.
Local Pride is also the name of the retailer's charity initiative, which is given a proportion of the takings from products in the Local Pride range to finance projects such as local football teams.
The initiative does not cost the independent stores any money because the donations are made possible by deals struck between Costcutter's trading teams and its suppliers.
Previous television activity has focused on a products and price message. This year the brand has spent between £3m-£4m on media and ran television activity in 36 weeks this year.
Media planning and buying is handled by Alchemy Media and Costcutter uses specialist store design agency called Design for Retail.
Follow Matthew Chapman at @mattchapmanuk