Staffordshire-based Britannia was behind the first remutualisation of a former building society when it bought Bristol & West's £4.5 billion savings business yesterday.
It also acquired B&W's 97 branches and 850 staff in a £150 million deal with Bank of Ireland which took over Bristol & West in 1997.
Britannia will gain 850,000 new customers.
Under the terms of the Financial Services Act the deal will have to get formal approval from the High Court but Britannia chief executive Neville Richardson expects completion by the autumn.
"It marks a step change in the scale of the business, which will grow by a third in terms of members, savings balances and branches.
"The customer base will grow to three million, assets to £30 billion and the branch network to more than 250."
Bank of Ireland is ditching the high street savings market to concentrate on mortgages, business finance and a distribution deal with the Post Office.
It will retain Bristol & West's mortgage book, 96 per cent of which is handled through financial intermediaries and rights to the Bristol & West name.
For Britannia, the deal marks a move into 65 towns and neighbourhoods where it is not currently represented.
Britannia and B& W branches within one mile of each other will be merged, including those in Birmingham, Solihull and Hereford, there will be no compulsory redundancies.
Britannia said the acquisition would be good for B&W staff.
"Every B&W employee will be offered a new role and there will be no compulsory redundancies," it said.
Cost savings will flow from merging branches, more efficient processing and integration of the two groups' systems.
Britannia said B&W's customers would become members and co-owners of Britannia and would be transferred into Britannia accounts.
"Most will be better off as a result and Britannia has pledged that none will be worse off," it said.
Mr Richardson added: "Strategic deals like this do not come along very often and it will significantly increase the size and scope of Britannia's business. This is the first major re-mutualisation in the UK, following the demutualisation trend in the late 1990s.
"As a result, B&W's customers will once again enjoy all the benefits of owning their savings provider, including a commitment to keeping an extensive branch network, competitive rates, an annual share of profits and a one member- one vote constitution."
BoI chief executive Brian Goggin said the disposal represented the delivery of a commitment that it gave in November.
"This is an excellent result for BoI and for the customers and employees of the B&W branch network," he said.
"To sell at a good price to a quality institution while enhancing the offer to customers and maintaining employment is good news for everyone."
The deal was welcomed by the Building Societies Association, which speaks for the country's 63 remaining mutuals.
"This is really good news, not only for the building society sector but also for the customers of Bristol & West," spokeswoman Rachel Blackmore said.
"They are going back into an organisation where effectively they will be the owners of the company."