The deal, termed Project Verde by Lloyds chief executive Antonio Horta-Osorio, will see Lloyds sell off 632 branches with around five million customers, representing six per cent of the UK branch network.
The two firms have agreed on commercial terms and are awaiting approval from respective boards, satisfactory documentation and further discussions with the FSA, HM Treasury and the European Commission.
Co-operative Group was the exclusive bidder for many months until a revised bid from rival NBNK Investments in May.
NBNK has since announced the firm will be wound-up, saying there were no other banking assets in the UK for sale that would meet the company's objectives.
NBNK chief executive Gary Hoffman said: "We are disappointed that the door has now been closed on this opportunity, with the result that we will be unable to deliver our vision of banking, bringing a vibrant new challenger to the high street, devoted to providing the level of service that customers want and deserve."
The Project Verde sale is a requirement by the European Commission in return for Lloyds receiving state aid in 2008.