The supermarket giant was granted an alcohol licence in October for the premises of Declans on 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 just a few hundred metres away at Matrix House on the edge of the village.
Usually, a change-of-use planning application is required to open supermarkets, but after the government has simplified the planning process.
Because the premises is already used as a shop, Sainsbury's did not need to apply - a move which locals said removes any chance of opposing the plans in an official capacity.
And after being granted the booze licence, Sainsbury's has now been successful in applying to have air conditioning and a refrigeration gas cooler on the roof.
They already have approval for other minor alterations, including external alterations and signage.
The move to open the supermarkets was heavily criticised, with the concerns led by ward councillor, Charlie Keith.
While he says it could put strain on long-serving local traders, he fears it could also threaten the village Post Office.
Located at the Premier shop on Wrenthorpe Road, he said its loss was described as "immeasurable".
Coun Keith said: “Every time you decide to get your tin of peas from Sainsbury’s, it could be putting the Post Office at risk.
“If we lose the Post Office, we will have a nightmare to get a sub post office back again. It’s a vital part of the community.
“This is driven by greed, not need, there’s no need for convenience shops. We’re alright as we are.”