The deal comes after weeks of negotiations with bond-holders in the bank who had faced taking a financial hit on their investments.
Originally Co-operative Group, headed by Edinburgh-born Euan Sutherland, outlined a rescue plan where it would contribute £1bn gathered from disposals and restructuring and fund another £500 million by writing down the value of its bonds.
Mr Sutherland had previously suggested there was "no plan B" to the proposal he unveiled in June.
However, an influential group of bondholders, including US hedge funds Aurelius Capital and Silver Point Capital, appear to have changed his mind as yesterday Co-operative Group admitted the recapitalisation plan will be "materially different".
Mr Sutherland, who ran do-it-yourself chain B&Q before joining Co-operative Group in May, said: "We have reached an agreement in principle which saves the Co-operative Bank.
"This is the first bank to be rescued and to survive as a standalone entity without taxpayer money."
The proposals are believed to meet new European directives which force bondholders and depositors, rather than taxpayers, to bear the cost of failed banks.
Co-operative Group will be the largest single shareholder in the bank - which will float on the stock market - with Mr Sutherland pledging to retain its ethos.
He said: "We are embedding Co-operative principles in the constitution of the bank to guarantee this."
But Andre Spicer, professor of organisational behaviour at Cass Business School, questioned whether Co-op can stay true to its roots once it is beholden to shareholders in the open market.
He said: "It is unlikely that the Co-op will maintain its ethical approach in the long run.
"History suggests that once a mutual bank is privatised it drops the focus on doing good to focus on doing well for shareholders.
"Private control of the Co-op will also have other outcomes. The number of staff the Co-op employs is likely to drop as management search for efficiencies. Staff who remain are likely to find themselves loaded down with various restructuring efforts."
It is expected the existing management of Co-op Bank will continue in place. Many of the bad loans it has on its books, particularly in commercial property, came from the takeover of Britannia Building Society in 2009.
Co-op then embarked on the failed Project Verde deal to buy more than 600 branches from Lloyds Banking Group.
Most of the executives who were in charge at Co-op Bank in that period have now left.
Further details on the exact offers to bondholders are likely to be revealed before the end of the month but Mr Sutherland said the Group had been working to "build a fair and attractive proposal for small investors".
It is expected small retail investors will be given an option to get an income bearing financial product while institutional investors are thought likely to take equity.
Mark Taber, who has campaigned on behalf of retail investors, said: "If they are being offered a bond, the terms will be important.
"They will need to consider how it's going to be structured and approached and the mechanics of it and make sure people aren't treated unfairly within it or left out."
A stock market listing of the bank - which has 4.7 million customers and employs 10,000 people - is likely to happen towards the end of this year or early next year.
Co-op Bank's bonds were suspended from trading on the London Stock Exchange at the bank's request.
The bank said it would request the suspension be lifted when the full details of the recapitalisation plan are announced.
Separately, Co-op Bank confirmed it was setting aside a further £105m for customer compensation. It said this is related to areas such as personal payment insurance mis-selling, arrears charges, processing of certain mortgage interest payments and what was described as a "technical" breach of the Consumer Credit Act.