Rumours that the Meanwood branch would shut have been circulating since August, when a consultation with employees began.
Today Asda confirmed the closure and added that the store was underperforming.
Three-quarters of the 36 staff have been found roles elsewhere in the company.
Senior vice-president of operations Anthony Hemmerdinger said:
“Despite the very best efforts of our colleagues in Asda Meanwood the store sadly continues to underperform in a tough market. The store site has recently reached the expiry of its current lease and so it made sense for us to consider its future.
“Following a consultation process we’ve made the difficult decision to close the store. We expect approximately three quarters of our colleagues to be redeployed to other Asda stores in the area and we will continue to work closely with the remaining colleagues to look at alternate opportunities.”
The Meanwood store is close to both Waitrose and Aldi branches.
Earlier this year Asda reassured staff at its Asda House head offices in Leeds city centre that the HQ would not close if a merger with rival chain Sainsbury's goes ahead.