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A vote on the scheme, which is designed to make those running English football more representative of the game as a whole, took place just an hour into a meeting at Wembley Stadium.
But the plans will still need to gain a 75 percent majority at the FA's annual general meeting on May 18 before they can be put into action.
There have long been calls for reform from both inside and outside the FA, but the thinly veiled threat from Britain's sports minister Tracey Crouch that millions of pounds of government funding for grassroots football would be withdrawn if there was no change appears to have prompted action.
In February, the House of Commons passed a "no confidence" vote in the FA's ability to reform itself.
But FA chairman Greg Clarke, who succeeded Greg Dyke in August, has threatened to resign if his reform proposals are rejected.
Under his scheme, the FA board -- its 'cabinet', with the Council its 'parliament' -- will be reduced from 12 members to 10, with three positions reserved for women by 2018.
Board members will be restricted to three-year terms, with Heather Rabbatts currently the only woman member.
There will also be changes to the council, with 11 new members added to better reflect what the FA has described as "the inclusive and diverse nature of English football".
This is likely to mean more black, Asian and minority ethnic members, as well as greater numbers of women and increased representation for disabled football and supporters' groups.