Euan Sutherland suggested that the organisation, which runs a bank, supermarkets and funeral homes, could not be turned around unless it adopted a more commercial approach.
Mr Sutherland had been brought into the business ten months ago at a time when the group was suffering from a £1.5 billion capital hole in its banking business.
The group was also hit by a drugs scandal involving the bank’s ex-chairman Paul Flowers, a Methodist minister.
Mr Sutherland wanted to reform the governance of the organisation, which is owned by its 7.2 million members and promotes an ethical approach to business.
Earlier this week he tended his resignation in a letter, which, according to reports, said the group was “ungovernable”.
His resignation was accepted by the Co-op and Mr Sutherland will be replaced on an interim basis by Richard Pennycook, the group’s chief financial officer.
Mr Sutherland’s fight with parts of the board had become increasingly public after they resisted his efforts to turn the group into a more conventionally run business, such as the retailer Tesco or department store John Lewis.
Mr Sutherland wrote on the group’s page on social network Facebook at the weekend that unidentified board members were seeking to undermine him by leaking details of his £3.7 million pound pay package – more than double his predecessor – to the media.
“We appear to have disaffected people who are determined to make life difficult and embarrassing for the Co-operative,” he said.
In his resignation statement, Mr Sutherland said he would not be taking the “retention payments and long-term incentive payments” that had been earmarked for him.
Mr Sutherland said: “It is with great sadness that I have resigned as chief executive. I have given my all to the business and had hoped to be able to lead its revival. However, I now feel that until the group adopts professional and commercial governance it will be impossible to implement what my team and I believe are the necessary changes and reforms to renew the group and give it a relevant and sustainable future.
“Saving the Co-operative Bank and with it the Co-operative Group from administration was a huge task, but the changes required do not stop there, with fundamental modernisation needed to safeguard the future for our 90,000 colleagues and millions of members.
“The group must reduce its significant debt and drive major efficiencies and growth in all of its businesses, but to do so also urgently needs fundamental governance reform and a revitalised membership.
“I will not accept the retention payments and long-term incentive payments previously agreed for the delivery and protection of value in the group and the bank, even though this was successfully delivered.
“I would like to thank all of the Co-op’s hard-working colleagues for the support they have given me during my time. I wish them all well. The Co-operative has some wonderful people who deserve a great future.”
The Co-op confirmed he will forgo a £1.5m bonus and long-term incentive payments due to him for securing the future of the Co-op Bank.
However, he picked up more than £2m in 2013 after earning more than £1m in pay and benefits between May and December, as well as a further £1m in compensation for shares he was due in his previous role at B&Q, which is owned by Kingfisher.
Co-op chairwoman Ursula Lidbetter said: “It is with deep regret that I accept Euan’s resignation. Last year, Euan and his team saved the the Co-operative Bank, without recourse to the taxpayer, and in doing so rescued the group from the biggest crisis in its 150-year history.
“They have worked night and day to renew the organisation and to give it a sustainable