The 40,000sq ft shop on Duke Street, in Leith, will remain a Scotmid until early May, before Tesco takes over and refurbishes the building.
Scotmid management said the store, where 86 people are employed, no longer fits into the company's strategy.
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Hide AdChief executive John Brodie said: "The strategy is to become Scotland's preferred community convenience retailer.
"Our Leith supermarket – the largest store we have – did not fit into that strategy."