It would also be the largest retailer in Europe, dwarfing Marks & Spencer, which is worth pounds 12bn, and the tenth largest in the world.
The company, to be be called Kingfisher, pledged to use its financial muscle to offer good deals to consumers.
"Both companies believe the potential benefits of the merger would enable the enlarged group to further improve their commitment to offering customers the best possible choice and service as well as permanently low prices," Kingfisher and Asda said.
The deal, announced in the City yesterday, is likely to see the companies selling each other's merchandise. Asda's George range of clothing would be sold in branches of Woolworths.
Kingfisher's Superdrug toiletries and Comet electrical goods could be sold in Asda's superstores. The combined group would have significant shares in sectors such as children's clothing, CDs and videos, increasing pressure on high-street competitors.
It would have a total of almost 3,000 stores, easily the largest chain in Britain. Kingfisher has 2,742, including 786 Woolworths, 70 Superdrugs and 290 B&Qs. Asda has 227 supermarkets.
Kingfisher emerges as the senior partner in the merger, with its shareholders set to control two-thirds of the shares in the new group. The deal follows a break-down in merger talks between the companies last year, while in 1997 Asda held merger talks with Safeway.
There has also been speculation that Wal-Mart, the US hypermarket retailer, might be preparing to invade the UK market and that Asda could be a target.
City analysts were yesterday speculating that there could still be a rival bid for Asda by Carrefour, the French hypermarket retailer. On the stock market shares in other supermarket operators such as Tesco and Sainsbury's rose in trading yesterday on the possibility of further bid action.
The Kingfisher-Asda merger comes at a sensitive time for UK retailing.
Britain's pounds 60bn supermarket sector was referred to the new Competition Commission last week on grounds of alleged profiteering.
UK retailers have been subjected to an extended campaign against supposed "rip-off" prices, with commentators pointing to far lower prices for food and clothing elsewhere in Europe and in the United States. Analysts said the merger could be delayed by a competition investigation, though one said: "I can see no grounds for one."
The company will be run by Sir Geoff Mulcahy of Kingfisher, who will be chief executive of the combined group. Allan Leighton, Asda's chief executive, will be his deputy. Archie Norman, Asda's chairman, and a former finance director of Kingfisher, will be non-executive deputy chairman.
The deal caps a remarkable comeback by Asda, which was on the brink of collapse in 1992 before Mr Norman came in to run it. It has grown rapidly since then to become Britain's third-largest supermarket group, behind Tesco and Sainsbury's.
Kingfisher and Asda said they will give more merger details on Monday.
MEGASTORE: ANATOMY OF THE WORLD'S TENTH-BIGGEST RETAIL GROUP
Almost 80,000 staff are employed in 242 locations. Its turnover for 1997-98 was pounds 7.6bn and profits were pounds 404m
Shoppers are greeted by clucking chickens and other gimmicks. Employees, who sport big, yellow badges, are called "colleagues" in a friendly, happy-clappy environment
Shoppers could soon be able to buy Superdrug, Comet and Woolworths products. Will boost Asda's chances of challenging Tesco and Sainsbury's, its larger rivals.
Family retailer employing some 30,000 at 787 outlets. Turnover of pounds 1.76bn and profits of pounds 114.4m for1998-1999.
High-street stalwart all over Britain. Cheap-and-cheerful stores using tried and trusted formula of selling everything from pick-and-mix sweets to children's clothing.
Asda's George clothing range might line up alongside Woolies' own Ladybird label. Woolworths' products could similarly find their way on to Asda's shelves.
About 12,000 staff employed at more than 700 stores. pounds 798.5m turnover and pounds 41m profits (1998-1999).
New "Concept" stores have moved towards swish, health-and-beauty emphasis. Stores have wooden floors and boast of a "chatty, magazine style of communication"
Allied to Asda, the chain could gain ground on its larger rival Boots and add significantly to the 4.5 million customers it attracts every week.
Employs almost 9,000 people in 270 stores. pounds 862.4m turnover and pounds 33.4m profits (1998-1999)
No-frills electrical retailer with emphasis on low cost, struggling to match the turnover of powerful rivals such as Dixons.
Alliance with Asda will give it more purchasing power, enabling it to compete more successfully with its rivals and possibly bringing down the price of electrical goods.
Employs 14,563 people at 290 stores. pounds 1.9bn turnover and pounds 188m profits (1998-1999)
User-friendly format for the weekend home-improver. Stores come in two formats, the smaller "supercentre" and 37 larger "warehouses", located mainly out of town.
Potential for loyalty scheme incorporating Asda and Britain's largest DIY retailer. Will not be as obviously affected as other Kingfisher companies.Reuse content