The Competition And Markets Authority (CMA) is due to publish its final verdict on the £14billion tie-up that would turn the UK's Big Four supermarkets into a Big Three.
The CMA previously said the merger would create a "substantial lessening of competition at both a national and local level".
Sainsbury's and Asda had offered to sell up to 150 stores in order to address competition concerns, and argued shoppers would be deprived of lower prices if the merger were blocked.
Sainsbury's, Walmart and Asda said they had mutually agreed to terminate the transaction, opting not to challenge the CMA's ruling through the Competition Appeal Tribunal, a specialist judicial body, which could have thrown it back to the CMA.
"The specific reason for wanting to merge was to lower prices for customers".
Mike Coupe, Sainsbury's chief executive, said that the CMA's conclusion "ignores the dynamic and highly competitive nature of the grocery market". "The CMA is today effectively taking 1 billion pounds out of customers' pockets".
Shares in Sainsbury's tumbled over 5% in morning trade to 214.4p.
But there were fears suppliers could get squeezed as the merged chain's buying power increased.
The move to reject the merger marks the first major decision the CMA has made since the appointment of former Tory MP Andrew Tyrie as chairman.
It remains unclear where the duo go from here, but it is understood that Walmart will continue to look to sell Asda to another buyer.
Walmart boss Judith McKenna said: "While we're disappointed by the CMA's final report and conclusions, our focus now is continuing to position Asda as a strong United Kingdom retailer delivering for customers".
There was no immediate sign, despite rumours of a private-equity sale, that the USA retailer Walmart would dispose of Asda in a kneejerk reaction to the collapse of the merger.
Asda boss Roger Burnley said he was "disappointed" at the CMA's decision.
Coupe said he was confident in Sainsbury's strategy despite the deal's prohibition.
He later apologised, calling it an "unfortunate choice of song" from the musical 42nd Street.