Lloyds Banking Group has agreed terms in the deal to sell 632 branches to the Co-op after a long-running takeover battle, the Telegraph reports.
The branches, known as Project Verde, had to be sold off under European Union state aid rules following its 2008 government bail out.
The branches are expected to be sold for between £1bn and £1.5bn.
Rival bidder NBNK will now be wound up, the paper reported.
The Verde business has about 5 million customers and represents 6% of all bank branches in the country.
