The all-share deal will create the world's biggest manufacturer of process control and automation equipment, with combined sales of pounds 8.7bn, pre-tax profits of pounds 1.3bn and a 10 per cent share of the market.
The merger will also result in 5,000 job losses from a worldwide workforce of 125,000. About 900 of these will be in the UK, where Siebe and BTR employ a total of 22,000.
The two companies said the merger would generate savings of pounds 250m a year after three years. Over the same period there would be one-off costs of pounds 400m, mainly as a result of the rationalisation programme.
Shares in both companies soared on news of the deal, increasing the market capitalisation of Siebe and BTR to pounds 5.1bn and pounds 4.3bn respectively. The announcement also helped the FTSE 100 Index of leading shares to close 130.9 points higher at 5848.4.
Shareholders in Siebe will emerge with 55 per cent of the combined group and BTR with 45 per cent. Three of the top five jobs - chairman, chief executive and chief operating officer - will also be taken by Siebe executives.
Ian Strachan, the chief executive of BTR, will take the post of deputy chairman but he is not expected to stay once the process of integration is complete.
Despite this, both companies were at pains to stress that the deal was not a takeover of the underperforming BTR by Siebe. Nor would the merger result in any culture clash between the two businesses.
"I feel very comfortable that this will be a blending of management teams," said Allen Yurko, who is chief executive of Siebe and will become chief executive of the merged company.
Although the merged company has a working title of BTR Siebe, the aim is to come up with a new name and identity for the combined group by February, when the merger is due to be completed.
The merger will create the world's number one provider of "intelligent automation" systems for manufacturing, process controls, power systems and industrial drives.
The combined company will leapfrog rivals such as Siemens, ABB and Emerson.
There is speculation, however, that the combined group's automotive business, which is mainly made up of BTR operations, will be sold off.
It has sales of pounds 1.64bn and 28,000 employees and produces automotive sealing, vibration and fluid systems.
The Siebe chairman, Lord Marshall, approached his opposite number at BTR, Bob Bauman, suggesting a merger about a month ago. The merger proposal was formally put during a meeting at the London offices of British Airways, where Lord Marshall is also chairman.
The respective chief executives and finance directors of the two companies were then brought in and the merger agreement was concluded in the space of about three weeks by a team of 15-20 executives and advisers.
BTR has underperformed the market by 80 per cent in the last five years, despite transforming itself from a sprawling conglomerate into a focused engineering group with a pounds 6bn disposal programme.
Over the same period, Siebe has fared much better, performing more or less in line with the market and consolidating its position in automation and controls through a $2.2bn acquisition programme, which has seen it swallow up Unitech, APV and Eurotherm.
The two companies said the merger would create "significant incremental growth opportunities" through the cross-selling of a wider range of products to their respective customer bases.
BTR Siebe will have a 13,000-strong salesforce and commanding positions in a number of market sectors.
It will be the world number one in automation, controls and power systems with market shares of 21 per cent, 18 per cent and 20 per cent respectively, and number four in the industrial drives and equipment market.
But Mr Yurko said the combined group did not envisage any regulatory problems from competition authorities.
Shares in BTR ended the day 40 per cent higher, while shares in Siebe rose by 13 per cent.
Shareholder approval will be required at extraordinary general meetings.
Separately, the American engineering conglomerate Tyco last night made an agreed $11.3bn paper bid for electronics group AMP.
The deal is the latest sign of the revival in merger activity in the US following the August stock market crash.
The white knight bid which trumps an earlier $9.8bn offer from AlliedSignal which was rejected by the AMP board will boost Tyco's market capitalisation to around $54bn.
Tyco has interests in medical supplies, electronics components and communications. The deal values AMP at $51 a share against a closing price on Friday of $44.125.
Tyco is best known for its ADT security systems and in the past 19 months has agreed to spend more than $13.4bn to expand its four main busineses.
In another US engineering deal, B F Goodrich agreed to buy Coltec Industries for $2.2bn or $20.13 a share.
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Derek Pain, page 23