Mr Sutherland's decision to quit comes after he complained that his efforts to overhaul the business had been made "impossible" by the mutual's failure to reform its governance.
He will be replaced by chief financial officer Richard Pennycook, who has been appointed as interim chief executive.
Mr Sutherland said he will not accept retention and long-term incentive payments due to him for securing the future of the Co-op Bank, which came close to collapse after it was found to have a £1.5 billion hole in its finances.
He said: "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."
He added: "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."
Mr Sutherland's decision to walk away comes after the Co-op's proposal to award him a £3.6 million pay deal was leaked to a Sunday newspaper.
In a Facebook post on Sunday, he expressed frustration that the story appeared to have come "from our group boardroom".
He added: "We appear to have disaffected people who are determined to make life difficult and embarrassing for the Co-operative at a time when what we need most are professionalism and loyalty to the business."
He offered to resign yesterday morning on a "point of principle", amid resistance to his plans to overhaul the troubled business after a year in which it faced the worst crisis in its history.
In an emergency call last night following the letter, board members agreed to a shake-up of its structure by splitting off representatives elected from its membership from the core "plc" type board overseeing the running of the business.
Co-op chair Ursula Lidbetter said she accepted Mr Sutherland's resignation with "deep regret".
She added: "Euan's resignation must now act as a catalyst for the real and necessary change which the group must go through."
Mr Pennycook, who was previously finance director at supermarket chain Morrisons, will lead the group while it searches for a permanent successor.
He said: "Our businesses continue to perform in line with the clear commercial plans put in place under Euan's leadership and I and the team will plot a steady course in the coming months."