Glaxo said the Wellcome Trust, a charitable organization that owns 39.5 percent of Wellcome plc, had agreed to accept the offer, which would be Britain's biggest takeover, subject to London High Court approval.
Wellcome said its board was meeting to consider the terms of the bid.
Glaxo is offering ?722 cash and 47 new Glaxo shares for every 100 Wellcome shares. At Friday's closing prices, this represents a 49 percent premium over Wellcome's closing share price of 688 pence.
Wellcome shares soared about ?3 on the news, touching a high of ?10 before easing back to 965.
But Glaxo shares fell, trading down 52-1/2 pence at 591 after a low of 585, as some analysts questioned the wisdom of the merger of two companies which both stand to lose U.S. patents on major drugs in 1997.
Wellcome's best-selling Zovirax, an anti-herpes drug, goes off patent in the U.S. in two years, while Glaxo could face generic competition to its ulcer drug Zantac, the world's biggest selling medicine.
Steve Plag, analyst at NatWest Securities, however, pointed to hundreds of millions of pounds the firms could save in annual costs by pooling their resources.
Glaxo chief executive and deputy chairman Sir Richard Sykes said the pharmaceutical industry was changing at an unprecedented pace. He said the enlarged group would benefit from a broader range of drugs, improved research and development prospects and potential for improved access to healthcare providers as health management systems develop.
There would also be significant opportunities to improve efficiency, and opportunities for non-prescription drug sales. "Wellcome shareholders are being offered full value as well as the opportunity to participate in a world leading pharmaceutical group," Sykes said.
Glaxo was already Europe's largest pharmaceuticals company in terms of sales. The merged group, to be called Glaxo Wellcome plc, will leapfrog U.S.-based Merck & Co Inc to become the world's biggest.
Glaxo, which has a cash pile estimated at some ?2.4 billion ($3.80 billion), had been expected to make some kind of move this year after staying on the sidelines last year as the shake up of the world's drug industry gathered pace.
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