The American-born lawyer is the first woman in the game to hold the position of club chairperson or president.
O'Neal won the vote on Thursday morning ahead of two fellow board members, former International Cricket Council and Cricket Australia chief executive Malcolm Speed and Maurice O'Shannassy.
"To be the first woman elected to this role, in the history of the competition, is deeply humbling," O'Neal said in a club statement.
"I think it says much about Richmond's progressive attitude, broad commitment to diversity, and in this instance, the important role females play in the game at all levels."
O'Neal has been on Richmond's board for eight years and came to Australia 24 years ago.
"After arriving in Australia, I was quickly attracted to Richmond and all that it stood for," she said.
"The Save our Skins campaign was in full swing and I could see a club with a long, proud history and great links into its community.
"I love the game and Richmond has been a passion of mine for more than two decades.
"It never occurred to me that I would one day be asked to serve the club in this way."
March officially stood down at Monday night's club best and fairest count after eight years in the role.
The Tigers are in strong shape, having made the finals for the first time since 2001.
"We have a management team that is building a strong off-field business and a football team that, under the guidance of (coach) Damien Hardwick, continues to improve," she said.
"The next five years are as important as the past five years.
"We must keep improving, on and off the field, and the board looks forward to providing the support and guidance to ensure this happens."
Speed and O'Shannassy said in the statement that they would support O'Neal as president.
Meanwhile, RIchmond has also re-signed Aaron Edwards, Jake Batchelor, Ben Griffiths and Todd Elton on one-year deals.