Haskell's resignation is effective immediately, while Randle and Weidner will remain for a few weeks to help with a leadership transition.
Read More: Emails reveal what Miss America Organisation really says about winners.
The organisation's board of directors said an investigation would be conducted after HuffPost published emails sent among executives and reported on deep dysfunction within the storied pageant organisation, The Washington Post reported.
After the report was published, 49 former Miss America winners signed a petition asking for the resignation of Sam Haskell, the pageant's chief executive, and the organisation's board of directors, including Washington media maven Tammy Haddad.
In one email published, a telecast writer told Haskell he would refer to all former Miss America winners as a crass word for female genitalia.
"Perfect," Haskell replied, according to the report. "Bahahah."
Haskell released a statement Friday night apologising for a "mistake of words," but he called the HuffPost story "dishonest, deceptive, and despicable."
The emails HuffPost reported are, at a minimum, indicative of deep fissures within the Miss America Organisation, a group known for lofty propriety and an aversion to scandal.
But it is no surprise that they've emerged as the "Me Too" movement has swept across the nation, bringing bad behavior to light in every corner of society.
"The language used and the attitudes toward the former Miss America's was completely shocking because they're usually treated with a lot of reverence," Hilary Levy Friedman, a professor at Brown University who studies pageant culture, told The Washington Post.
"The totality of it was quite surprising. And at this moment in American culture, this feels particularly weighty."
Caressa Cameron, a Fredericksburg, Virginia, native who held the Miss America title in 2010, in an interview with The Post said the problem was not one of language, but of respect and leadership style.
Haskell joined the Miss America organisation nine years ago after a successful career as a talent agent, and he is largely credited for bringing the pageant back to prominence.
But former pageant winners are claiming he ruled with an iron fist and shamed and blackballed women who didn't comply with his wishes.
Cameron said her troubles with Haskell began 30 days into her reign, after she invited a woman who had coached her to a homecoming party being thrown in Cameron's honor.
"Sam Haskell said I was not to invite her. She could not come. He basically threw a temper tantrum," she recalls. "And then he didn't come. He didn't come, along with very prominent members of the organisation and the board."
Cameron says the organization prevented her from participating in events related to her platform, HIV/AIDS prevention, and that she was once mistakenly sent an email in which Haskell referred to her mother as "uneducated trash".
Much of the HuffPost report focused on Haskell's ire with the 2013 Miss America, Mallory Hagan.
The article included emails in which Haskell makes insulting remarks about Hagan's body and sexual history. The story also includes emails attacking former winners Kate Shindle and Gretchen Carlson, the Fox News host who sued network chairman Roger Ailes for sexual harassment.
Cameron says she and a group of other former Miss America winners have organised to demand the resignations of the entire board and leadership team.
Haddad, who is quoted in some of the negative emails, had submitted her resignation from the board earlier in the year and made it effective immediately after the report was published Friday.
Cameron said she and the other former winners would like to see the reins of the pageant handed to Shindle and Carlson for temporary stewardship.
"I don't think it's the end," says Cameron. "Women who are this driven, this educated and this connected - we can definitely steer this thing and make it greater than it's ever been."
-AP and Washington Post.
