Staff were said to be reduced to tears on Thursday morning when they were told the news.
A spokesman for The Co-operative Food said: “I can confirm that we have agreed to sell our food store in Annan to Aldi.
“The Co-operative Group continually reviews its retail estate, and we have made the decision to focus on smaller convenience stores and sell those trading outlets that do not align with our strategy.”
He added: “The consideration to sell the store is in no way a reflection on the hard work and commitment from colleagues working at the Annan branch.”
Aldi issued the following statement: “We are pleased to announce that Aldi will be opening a store in the Annan area, following a purchase from The Co-operative Group.”
It added: “The new store, which is set to open in 2015, is part of our expansion strategy to help meet Aldi’s growing customer demand across the UK.”
The Co-operative movement has a long tradition as a retailer in the Annan district and has a large number of members and other customers.