Under the terms of this agreement, the Co-op will pay around Â£1.5 billion ($2.3 billion) to acquire the 632 outlets, as well as the company's TSB brand and its Cheltenham & Gloucester mortgage arm.
Senior officials from both financiers will now hold extensive talks regarding the finer points of the deal and, if these go well, the Co-op's banking business will increase in size by around 300 per cent to more than 900 branches across the country.
Acquisitions body NBNK also made an offer to the company - which acquired HBOS in 2009 to become Lloyds Banking Group - for these assets and Tim Tookey, interim chief executive of the lender, said both bids were "very competitive".
However, he added that the Co-op's presence in the financial market tipped the balance in its favour.
"The board felt the execution risks associated with an existing player were likely to be less," he stated.
By Claire Archer