The supermarket giant obtained an alcohol license in October for the Declans premises at the corner of Bradford Road and Potovens Lane in Wrenthorpe, near Wakefield.
Hundreds of people had signed a petition saying they did not want the supermarket to open on the site.
Another supermarket, Co-op, is planned a few hundred yards away at Matrix House on the outskirts of the village.
Usually, a change-of-use planning request is required to open supermarkets, but after the government has simplified the planning process.
Because the premises are already in use as a store, Sainsbury’s did not need to apply – a move which residents say removes any chance of objecting to the plans in an official capacity.
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And after obtaining the liquor license, Sainsbury’s has now successfully applied for the installation of air conditioning and a refrigeration gas cooler on the roof.
They already have approval for other minor changes including external changes and signage.
The decision to open supermarkets has come under heavy criticism, with concerns being led by City Councilor Charlie Keith.
Although he says it could put a strain on longtime local traders, he fears it could threaten the village post office as well.
Located in the Premier store on Wrenthorpe Road, he said his loss was described as “immeasurable”.
Councilor Keith said: “Anytime you decide to buy your can of peas from Sainsbury’s it could put the post office at risk.
“If we lose the post office, we’ll have a nightmare getting back a secondary post office. It is a vital part of the community.
“It’s driven by greed, not need, there is no need for convenience stores. We are fine as we are.