The Warner-Wellcome joint venture will sell a range of well-known medicines including Calpol, Actifed, Sudafed, Listerine, Sinutab and Anusol, which are all available without prescriptions.
It will also sell non-prescription versions of Zantac, the largest-selling prescription drug in the world, and Zovirax, the eighth-largest prescription drug.
Zantac, Glaxo's main profit-earner, and Zovirax, Wellcome's antiviral product, are currently available only on prescription in the UK.
Glaxo hopes to sell Zantac without prescriptions for treatment of heartburn but has yet to apply for approval to sell it over the counter. It will continue to sell it with prescriptions for treatment of ulcers.
Wellcome expects to be given approval shortly to sell Zovirax in the UK without prescriptions but has yet to apply for US approval.
All three companies have other prescription drugs they would like to sell without prescriptions. These include a Warner-Lambert drug for menstrual pain, a Wellcome antihistamine and a Glaxo hay fever treatment.
The news brought relief to investors in drug companies, who have suffered massive losses so far this year. Wellcome's shares rose by 31p to 696p, compared with a recent low of 600p, and Glaxo's gained 20p to 558p, compared with a low of 509p.
John Robb, Wellcome's chief executive, said the deal gave Wellcome's existing non-prescription business critical mass. 'We needed a first-class marketing operation.'
For Glaxo the arrangement provides a solution to its strategic dilemma, which has caused internal ructions epitomised by the sudden departure of Dr Ernest Mario, the former chief executive, in March. He had advocated buying a non-prescription business.
Dr Franz Humer, Glaxo's chief operating director, said the group's strategy was to concentrate on its prescription business but not to forgo opportunities in the over-the-counter market.
Warner-Wellcome will have sales of about pounds 1bn, based on last year's figures, and profits of pounds 150m, before the launch of non-prescription versions of Zovirax or Zantac. It will absorb a fifth of Warner-Lambert's business and a sixth of Wellcome's. The joint venture will employ a sales force of about 800, Mr Robb said.
It will be managed by Warner-Lambert from its New Jersey base in the US, and the American company will supply four of the seven board members. The partners have yet to decide where to site the European office.
Glaxo has formed a separate joint venture with Warner-Lambert under which it has agreed to supply Zantac and other over-the-counter versions of its drugs to the joint venture. Glaxo will receive a royalty on sales and a half-share in the joint venture's profits.
The sales of Glaxo's products will be handled by Warner-Wellcome, which means that Wellcome will have a small share of any profits on over-the-counter sales of Zantac.
In the US Warner-Lambert will receive 70 per cent of Warner-Wellcome's profits, and Wellcome the rest. Elsewhere in the world they will share the profits equally.
The two joint ventures were negotiated separately but in parallel. Mr Robb said he had been in discussions with Warner-Lambert since the start of the year but was told about the Glaxo deal only two months ago.
Dr Humer said Glaxo's talks with Warner-Lambert started four months ago and he was also told about the Wellcome deal two months ago. Both British companies said the involvement of the other strengthened the three-way partnership.
Mr Robb said there were no plans to float the joint venture. 'I anticipate it will take five years to get it running properly.'
The joint venture has been formed against the background of rising anxiety about growth prospects for prescription drugs businesses, with medical spending under pressure in the US and Europe. The over-the-counter business is less vulnerable to politically inspired cutbacks.