The chair of the Co-operative Group says the unanimous vote in favour of wide-ranging reforms as a "highly significant moment" for the mutual, which slumped to £2.5 billion annual losses after a period of crisis.
Ursula Lidbetter said: "I am delighted that our members have made clear their commitment to far-reaching reform of our governance with this unanimous vote.
"There is a huge task ahead of us if we are to deliver the reforms necessary to restore the Group's reputation and return it to health but the board will work hand-in-hand with our members to ensure that we seize this opportunity.
"It is vital that the right changes are put in place as soon as possible to build a more effective organisation for our members, customers and colleagues."
Britain's biggest union has welcomed the vote for reform of the troubled mutual.
Adrian Jones, national officer of Unite, said: "The vote for reform is a welcome step in the right direction and one which we hope will put the Co-op Group on the road to stability.
"Going forward it is vital that our members and employees have a voice in the reform process for it to succeed and ensure the Co-op Group has a fighting chance while retaining its unique values and ethos."
Former City minister Lord Myners wants to replace this with a slimmed-down "plc and beyond" structure staffed by professionally-trained directors.
The former Marks & Spencer boss was appointed a director of the Co-operative Group in December but announced he is to leave following this weekend's vote.
He has said it was apparent to him from the first time he attended a board meeting that not one of its members had the ability to address the complex issues faced by a group burdened with £1.4 billion of debt.
This weekend's ballot will be decided by representatives of its independent societies and affiliated organisations - who hold 22% of the vote - and others voting on behalf of its regional membership boards making up the remaining 78%.