On Monday, a resolution put forward by Shane Hogan and Brendan Burgess to begin the demutualisaiton process immediately was passed by 7,810 to 6,191.
It directs the board to advise Irish Financial Services Regulatory Authority by the end of the year of its intention to demutualise.
They said it was the first time in history that members of an Irish building society have succeeded in passing a resolution to commence demutualisation.
"We are delighted that members have sent the board a clear message that demutualisation must start this year, regardless of what happens with the proposed changes to the 1989 Building Societies Act.
"We are tired of waiting for the board to get the conversion process into gear, so we have been forced to direct them to get moving without further delay," said Mr Hogan.
"The board has sullied their own reputation in their management of this issue. They initially rejected the motion, until IFSRA insisted that it was legally valid. "Then ... they acted in a hypocritical and duplicitous manner by voting their open proxy votes against the motion, even though they had stated in the AGM papers that 'the board does not oppose this motion.'"
A separate resolution proposed by the board to demutualise was also carried by a wide margin.
Mr Hogan said he was against part of this motion as it made reference to payouts to staff and management of the society.
Mr Hogan also said that he hoped that the board will take the advice offered by several members at the AGM to beef up the board membership in preparation for the important conversion process that will commence later this year.
Mr Burgess has campaigned for the only seat on the board up for re-election that held by chairman Michael Walsh. He lost the vote by 71% to 29%.
The sale of Irish Nationwide could net members more than €7,000 each in windfall payments.
To be a member you must have at least €20,000 in a share account for two years or a minimum balance of €625 on a year for the same period. Anyone who joins the society now will not be eligible for a payout.