The deal creates the UK's largest company, valued at £130bn.
The new group, to be called Glaxo SmithKline, has said job losses are inevitable, but has declined to say how many will be cut.
Glaxo SmithKline will be headed by Jean-Pierre Garnier, currently number two at SmithKline, who takes the role of chief executive while Glaxo head Sir Richard Sykes is to be non-executive chairman.
Its headquarters will be in London, while its operational base will be in the US. It will be listed on both the London and New York stock exchanges.
Job fears
Unions fear the tie-up will mean up to 15,000 job losses worldwide out of a workforce of 105,000 and they are worried about the shift of operations to the US.
"Staff have been kept completely in the dark and we need to now know how a company whose chief executive is going to live in the United States is going to have the same commitment to a company that has traditionally been the jewel in the British pharmaceutical crown," Roger Lyons, general secretary of the Manufacturing, Science and Finance union, said.
Mr Lyons also warned of a possible transfer of European jobs to the US.
"The European Commission will need to look at the regional job implications," he said.
Fears about job cuts had already prompted the MSF union to ask for a meeting with company chief executives and Trade and Industry Minister Lord Sainsbury on 26 February.
Investors, though, have welcomed the deal. However, in early trade, Glaxo dropped 50p to £17.68 while SmithKline Beecham was down 39p to 8809p. The shares had risen sharply on Friday when the merger talks were confirmed.
Glaxo on top
Glaxo shareholders are to own 58.75% of the new group and SmithKline investors 41.25%.
The new group would have sales of £17bn and 7.4% of world pharmaceuticals markets.
Savings are expected to be considerable, with £250m savings expected to come from combining their research and development. The group expects total annual savings of £1.1bn.
The new company will have an annual research and development budget of £2.4bn, the largest in the world.
The merged group will bring together a host of top drugs for aids, diabetes and asthma as well as traditional consumer products such as Lucozade and Ribena.
The two companies have attempted to merge before.
Two years ago, talks failed after a reported clash of egos between Glaxo chief executive Sir Richard Sykes and his SmithKline counterpart Jan Leschly, who is now to retire early.
There has been a wave of mergers in the drugs industry recently, with the UK's other main drug company, Zeneca, merging with Sweden's Astra, while in the United States Pfizer is proposing a tie-up with Warner Lambert that would have created, until today's announcement, the world's biggest drugs company.