The takeover could result in a cash payout of pounds 600 or free RBS shares, to Midshire's 1 million-plus members which include up to 300,000 so-called "carpetbaggers".
Dr George Mathewson, group chief executive at RBS, said the takeover of Wolverhampton-based Midshires would virtually double the RBS residential mortgage book and increase its retail savings balances by 75 per cent.
"If there came along a very substantial deal on the same basis [as this], I do not think that anyone would say no to it. I do not know anyone who would say anything different," he added.
However, Jeremy Batstone, head of research at NatWest Stockbrokers, said: "RBS has traditionally been seen as the prey rather than the predator, although this appears not to be a hostile takeover. But Midshires is not big enough an acquisition to prevent RBS from still being seen as a potential target."
Birmingham Midshires, which has a residential mortgage book of about pounds 7bn, has about 1.1 million savers and 150,000 borrowers serviced through 115 branches. RBS, which operates through 660 branches, has slightly more savers and less borrowers. It also has 1.7 million current account holders and the bank's total assets stand at almost pounds 70bn.
The takeover had been widely anticipated since the society resolutely refused to rule the option out 18 months ago, at the time of flotation announcements by Woolwich, Northern Rock and Alliance & Leicester building societies.
Mr Batstone said: "It has been an open secret that [Midshires] was looking for a partner and has been everyone's favourite to be `carpetbagged'. It is yet another nail in the coffin for mutuality despite the recent Nationwide vote. The rest of the building societies are swimming against a tide which is coming in fast."
Mike Jackson, chief executive at Birmingham Midshires, said that the two organisations had come together only nine months ago, after a long- running review of the society's options concluded that a takeover by another institution made most sense.
"I think George [Mathewson] picked up the phone about a week before I did, but we had also concluded that RBS was the one we should be talking to," Mr Jackson added.
Although Midshires' mortgage processing centre in Bracknell, Berkshire, will close Mr Jackson pledged there will be no compulsory redundancies among staff. Midshires would continue to be run as a separate business, and its brand identity and branch network had been guaranteed for three years.
The takeover would allow for considerable cross-distribution of each organisation's services and financial products, which he said was needed by members of his society.
Mr Jackson denied that continual rumours about Midshires' intentions had led to "carpetbagging" on a mass scale, thereby diluting the value of any free payout to longer-term members. He said the new accounts had increased the value of Midshires to RBS and allowed for even greater cross- selling opportunities.
RBS said it was pricing the deal at a price/earnings ratio of 12 when the society is finally taken over next year. The deal will be financed by issuing new shares, which are to be taken up entirely by Scottish Widows, the Edinburgh mutual life insurer, lifting its stake in RBS to about 4.7 per cent.
RBS already collaborates with Scottish Widows over telephone sales of personal pensions.