Toby Young has announced he is standing down from the universities regulator saying his appointment has “become a distraction”.
The journalist turned educationalist apologised “unreservedly” for a string of controversial comments he had made on social media in recent years.
His announcement comes after ministers were forced defend his appointment in the Commons on Monday following backlash from MPs, including prominent Tories.
Writing in The Spectator, Mr Young said: “The caricature drawn of me in the last seven days, particularly on social media, has been unrecognisable to anyone who knows me.
“I am a passionate supporter of inclusion and helping the most disadvantaged, as I hope my track record of setting up and supporting new schools demonstrates.
“But some of the things I said before I got involved in education, when I was a journalistic provocateur, were either ill-judged or just plain wrong - and I unreservedly apologise.”
A petition calling for Mr Young to be sacked from the board of the Office for Students (OfS) has gathered more than 219,000 signatures.
Theresa May was forced in an interview on Sunday to address criticism about the appointment and said she had been unaware of his history of crude and sexist comments.
Education select committee chairman and Conservative MP Robert Halfon, who has cerebral palsy, attacked the “dark” and “dangerous” articles written by Mr Young in the past during an urgent debate in the Commons on the issue.
He said: “What I’m more concerned about is some quite dark articles where he talks about the disabled, where he talks about the working classes, and much more significantly in 2015 - and I have the article here - on what he calls progressive eugenics.
“Now, I find this incredibly dark and very dangerous stuff.”
Tory Sarah Wollaston called for Mr Young’s appointment to be reviewed, telling MPs: “I’m afraid I feel Mr Young’s comments do cross a line and are therein indicative of an underlying character and the kind of person that would tweet comments to a woman that talk about masturbating over images of refugees.”
Mr Young’s resignation from the newly-created post of universities regulator - much like his appointment - quickly provoked debate among senior politicians.
Mr Halfon said Mr Young had “done the honourable thing” in quitting.
But shadow education secretary Angela Rayner said: “The Toby Young saga has cast great doubt on the judgment of the PM, who failed to sack him in the first place.”
Universities minister Jo Johnson, who was forced to defend him in the Commons on Monday night, stood firm in his support of Mr Young, who is a champion of free schools, which were introduced by David Cameron’s administration.
Mr Johnson, who is Foreign Secretary Boris Johnson’s brother, dismissed Mr Young’s detractors as “armchair critics”.
He wrote on Twitter: “Toby Young’s track record setting up & supporting free schools speaks for itself.
“His decision to stand down from the OfS board and repeat unreserved apologies for inappropriate past remarks reflects his character better than the one-sided caricature from his armchair critics.”