Only one woman, Heather Rabbatts, currently sits on the board.
The reforms included reducing the board from 12 members to 10 and introducing limits so that nobody serves more than three terms of three years.
The FA said it also planned to add 11 new members to the FA Council "to ensure it better reflects the inclusive and diverse nature of English football".
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FA chairman Greg Clarke said last month he would step down if the government did not support his proposals to reform the under-fire governing body.
Sports Minister Tracey Crouch wants the FA, whose 120-member Council has been accused of being antiquated and resistant to change, to be more transparent and diverse.
"I am delighted that the FA board is able to unanimously recommend this strong package of reforms," said Clarke in a statement.
"They represent huge progress and, if approved following consultation, will ensure that The FA is meeting the requirements of UK sport governance best practice."
However, anti-discrimination group Kick It Out said the reforms were "a sham" that still failed to give sufficient representation to minority groups.
"By prioritising women on boards, all other protected groups are being left behind," said chairman Herman Ouseley in a statement.
"It is quite right for women to be progressing but these reforms need to be across the board and not just directed at women.
"Without proper representation of minority groups I would not trust these bodies to fully deliver transparent practices and the changes are likely to be a sham," added Ouseley.
The FA board has conducted a review of its corporate governance over the past six months as it seeks to serve better the long-term interests of the English game.
It said a special meeting of the FA Council will be convened on March 21 to debate the recommendations, with a formal vote scheduled for April 3. If majority approved, they will be voted on by shareholders at an annual general meeting on May 18.
(Reporting by Alan Baldwin, editing by Neil Robinson and Ken Ferris)
