Lord Myners, who was recently appointed senior independent director at the group, is conducting the review and will report back on the first phase by April.
That will involve making recommendations in areas such as strengthening board policies, composition and working processes.
Initial proposals are likely to be put forward at the Co-op's annual general meeting in May with a special meeting to approve any changes taking place later in the year.
The second part of the review, not due to be completed until the end of this year, will investigate ways to improve links with members, customers and staff.
It will also cover the governance of how Co-op works with other co-operative and mutual organisations.
Co-op has been affected by problems in its banking arm which eventually led to the bank accepting a £1.5 billion rescue proposal led by US hedge funds.
The bank, of which Co-op will retain a large but not controlling stake, is expected to be floated at some point this year.
The governance of the group has also been called into question amid drug allegations made against former Co-op Bank chairman Paul Flowers.
Lord Myners said: "The advantages of mutuality can't be taken for granted. There is a significant prize ahead if the group grasps this opportunity for change.
"We must demonstrate the highest levels of integrity in our board leadership and focus the group's energies on developing a winning customer offer."
Co-op is now run by Edinburgh-born chief executive Euan Sutherland, who only joined last May.
The terms of reference of the "forward looking" review were agreed at a board meeting earlier this week.