The Co-op store at the Meridian Centre in Peacehaven is to close next month.
A sign at the entrance said that the shop would shut for good on Saturday 20 January.
The closure comes with the Meridian Centre about to undergo an overhaul in a scheme that will, first, involve knocking down the existing buildings.
A new Morrisons supermarket is planned to replace the Co-op, with a number of other shops and a new public library.
And earlier this year, councillors unanimously approved the scheme for a “comprehensive redevelopment” of the shopping centre.
The supermarket chain, Britain’s fifth biggest, said that its new branch would create about 190 full and part-time jobs. It said that the Co-op had 46 staff at the site.
The revamp is expected to create 200 other jobs – up from 60 at present – and Morrisins said that the 390 jobs in all would be worth up to £4 million a year in salaries alone.
The company is also looking to add some housing on the eastern edge of the site at a future date.