Sainsbury's said there are no planned store closures as part of the deal, with both brands to operate side by side.
The combined supermarket expects to lower prices by around 10 per cent on products customers buy regularly.
It will see Asda owner Walmart hold 42 per cent of the new business and receive £2.97 billion in cash, valuing Asda at £7.3 billion.
Sainsbury's is valued at around £5.9 billion.
The new supermarket group will have combined revenues of £51 billion and will aim to generate £500 million in cost savings.
David Tyler, Sainsbury's chairman, said: "We believe that the combination of Sainsbury's and Asda will create substantial value for our shareholders and will be excellent news for our customers and our colleagues.
"As one of the largest employers in the country, the combined business will become an even greater contributor to the British economy.
"The proposal will bring together two of the most experienced and talented management teams in retail at a time when the industry is undergoing rapid change."