The three nations were given full-time seats on the International Cricket Council's (ICC) decision-making executive committee in January 2014.
However, that decision was reversed at a meeting in Dubai on Thursday.
ICC chairman and India board president  Shashank Manohar said: "No member of the ICC is bigger than the other."
Manohar, who replaced Narayanaswami Srinivasan at both the Board of Control for Cricket in India and the ICC, was among critics who said the 'Big Three' would take over the sport at the expense of other nations.
He has promised "a complete review" of the constitution and will be in charge of a five-member steering group which will look to put together recommendations to proposed changes at the ICC's annual conference in June this year.
"I am determined to make a meaningful contribution in this regard with support of all the members," Manohar said before adding the ICC chairman would not be allowed to hold a position in a member country board in future.
Meanwhile, the ICC has also reinstated Sri Lanka as a full member after the country held elections last month to appoint a new organisation to run the sport.
Sri Lanka had previously been sanctioned for government interference.
The power of England, Australia and India in world cricket is to be reduced as part of reform measures introduced by the sport's governing body.