The bid is expected to mean thousands of jobs will be lost at Warburg, once Britain's premier merchant bank.
But the deal will not include Mercury Asset Management (MAM), the highly profitable fund management group.
Only two Warburg directors remain on the new seven-strong executive committee of what will be known as SBC Warburg.
SBC chief executive Georges Blum, announcing the proposed deal in London, said that although there was "overlap" between the two banks, it was too early to say what job losses there might be.
Forecasts that thousands of jobs will go, particularly in Warburg's back office and securities activities, were strengthened by a report from Zurich quoting SBC documents.
"Lay-offs will be unavoidable but we do not know the exact number at the present time," they said.
Both sides played down the possibility of a counter-bid, despite persistent market rumours that NatWest may make a higher offer. NatWest would want to buy the whole group including the 75 per cent stake in MAM. Under the SBC deal, MAM's shares will be returned to Warburg's shareholders, and it will become an independent company worth at least £1.5bn.
Sir David Scholey, Warburg's chairman and chief executive, survives as non-executive chairman. He said bonuses would be paid to Warburg staff to encourage them to stay with the newly merged outfit.
Sir David played down the intense speculation over future ownership of MAM. "Mercury is becoming a widely held and extremely independent public limited company, with a very strong capital base and a very strong capital record," he said. "There is no reason for that not to continue."
Sir David hinted the Warburg board would oppose any rival bid: "I do not see any reason at all why anyone would seek to interfere or impose themselves on this transaction."
A City source said separately that although the SBC offer had an 85 per cent chance of succeeding, there was still a possibility of a higher bid from NatWest.Sir David pointed to the £63m premium to market value which SBC is paying. He also said the reaction of Warburg staff to the SBC deal worldwide had been "positive".
Marcel Ospel, SBC's global head of international business, negotiated the deal and will move to London as SBC Warburg's chief executive. The deal will be in two parts, starting with a cash payment of £860m to Warburg. This is subject to approval by a Warburg shareholder vote later this month.
Then, a "scheme of arrangement" will be launched, through which Warburg will distribute at least £3.65 in cash and 0.538 MAM shares for each Warburg ordinary share, equivalent to not less than 850p per share. The cash and shares will be payable in August. This values the whole of the Warburg group at £2.2bn.
Sir David told journalists at SBC's London office that the two companies "fit like the clunk of a Rolls-Royce door". SBC chief executive Georges Blum described the fit as "wonderful".
When Warburg's recent merger talks with Morgan Stanley fell through, Sir David put together a five-strong executive committee; only three are in the new set-up. SBC Warburg's executive board will be headed by Mr Ospel. Warburg's Mark Nicholls will continue to head up corporate finance. Colin Buchan will lead equities together with SBC's Markus Granziol. he rest are SBC: Gary Brinson, Global Institutional Asset management; David Solo, Rates (fixed interest business); and Andrew Siciliano, foreign exchange.
Warburg and MAM brought their 1994 results forward by two weeks to coincide with yesterday's announcement; Warburg made profits before exceptionals of £42.1m, a fall from £297m the last time. Investment banking plunged to a loss of £16.9m, compared to MAM's profit of £111.5m, £2m up from last time.
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