The Bank confirmed Charlotte Hogg had resigned within minutes of the Treasury Select Committee declaring her "professional competence falls short" of the standards required.
Former chancellor George Osborne said on Twitter (Frankfurt: A1W6XZ - news) that her departure was a "real loss to public life" and questioned whether she would have gone "if she had been an older man whose sister worked at a bank".
The committee's damning report came after Ms Hogg's admission that she had failed to inform the Bank, when she joined as chief operating officer in 2013, that her brother, Quintin, worked in a senior strategy role at Barclays (LSE: BARC.L - news) .
The failure came to light after she filled in a questionnaire for the committee as it scrutinised her promotion to deputy governor - a job that would give her oversight of bank regulation.
Following checks, she admitted the omission breached the Bank's guidelines - which she had helped draw up - covering potential conflicts of interest.
Ms Hogg, a member of the Bank's nine-strong Monetary Policy Committee (MPC), will still take part in this week's interest rate decision
She is remaining at the Bank for a transition period but it is possible that she leaves before a new MPC member is appointed.
That could leave the committee down to eight for several months as the Treasury seeks a replacement. The MPC's next meeting after this week will be in May.
Ms Hogg has waived her entitlement to three months' salary, or around £65,000, that she would be entitled to, covering a period of "purdah" on leaving the Bank.
The deputy governor is the daughter of Douglas Hogg, the third Viscount Hailsham and former cabinet minister, who reached the Bank after a career in the private sector that took in senior roles at many major banks.
In its assessment of her actions on Tuesday, the Treasury Select Committee stopped short of recommending she be fired.
But in her resignation letter to Bank governor Mark Carney and chairman of the Bank's Court, published by the Bank, it was confirmed she had already volunteered to go but that request had been turned down.
She wrote: "Last week I offered you my resignation in recognition of the fact that I made a mistake in not declaring my brother's work on the forms that the Bank requires. It has become clear to me that I should now insist.
"As I have said, I am very sorry for that mistake. It was an honest mistake: I have made no secret of my brother's job - indeed it was I who informed the Treasury Select Committee of it, before my hearing.
"But I fully accept it was a mistake, made worse by the fact that my involvement in drafting the policy made it incumbent on me to get all my own declarations absolutely right.
"I also, in the course of a long hearing, unintentionally misled the committee as to whether I had filed my brother's job on the correct forms at the Bank.
"I would like to repeat my apologies for that, and to make clear that the responsibility for all those errors is mine alone."
Mr Carney said in response: "While I fully respect her decision taken in accordance with her view of what was the best for this institution, I deeply regret that Charlotte Hogg has chosen to resign from the Bank of England."
The select committee's chair, Andrew Tyrie MP, said: "This is a regrettable business with no winners.
"Ms Hogg has acted in the best interest of the institution for which she has been working. This is welcome."