Dame Lowell Goddard has resigned as Chair of the Independent Inquiry into Child Sexual Abuse, the Home Secretary has confirmed.
It comes amid reports she spent three months on holiday or abroad in her first year in the £500,000 job.
The Home Secretary, Amber Rudd, reassured victims of abuse that "the work of the inquiry will continue without delay and a new chair will be appointed".
Dame Goddard, a New Zealand judge, was appointed after two previous chairwomen quit.
The inquiry was established in 2014 to look at claims of a cover up by the establishment, after allegations a paedophile ring operated in Westminster in the 1980s.
It has yet to hear any evidence from witnesses.
Dame Goddard's letter reads: "I regret to advise that I am offering you my resignation as Chair of the Independent Inquiry into Institutional Child Sex Abuse, with immediate effect. I trust you will accept this decision."
Peter Saunders, chief executive of the National Association of People Abused In Childhood, told Sky News he was "profoundly disappointed".
"She has been hounded somewhat by the press and I think that is very regrettable and that is what the British tend to do I am afraid," said Mr Saunders.
"I think its a great tragedy she has gone but let's move on."
Dame Goddard spent 44 days in Australia and New Zealand in the inquiry's first year, a spokesman has confirmed.
But he told the Times she had been on "inquiry business" and learning from a similar Australian abuse inquiry.
On top of the time spent abroad, the judge also received 30 days' annual leave.
Her annual salary was £360,000 and she also got £110,000 to rent a flat and £12,000 for utility bills.
The Government also funded four return flights to New Zealand for Dame Goddard and her husband.
In accepting the resignation, the Home Secretary said the inquiry had "already instituted and made progress on its three core projects: the Research Project, the Truth Project; and the Public Hearings Project".
She thanked the judge for "bringing your experience to bear" and for 16 months of "commitment" and "hard work"
The Home Secretary, Amber Rudd, reassured victims of abuse that "the work of the inquiry will continue without delay and a new chair will be appointed".
Dame Goddard, a New Zealand judge, was appointed after two previous chairwomen quit.
The inquiry was established in 2014 to look at claims of a cover up by the establishment, after allegations a paedophile ring operated in Westminster in the 1980s.
It has yet to hear any evidence from witnesses.
Dame Goddard's letter reads: "I regret to advise that I am offering you my resignation as Chair of the Independent Inquiry into Institutional Child Sex Abuse, with immediate effect. I trust you will accept this decision."
Peter Saunders, chief executive of the National Association of People Abused In Childhood, told Sky News he was "profoundly disappointed".
"She has been hounded somewhat by the press and I think that is very regrettable and that is what the British tend to do I am afraid," said Mr Saunders.
"I think its a great tragedy she has gone but let's move on."
Dame Goddard spent 44 days in Australia and New Zealand in the inquiry's first year, a spokesman has confirmed.
But he told the Times she had been on "inquiry business" and learning from a similar Australian abuse inquiry.
On top of the time spent abroad, the judge also received 30 days' annual leave.
Her annual salary was £360,000 and she also got £110,000 to rent a flat and £12,000 for utility bills.
The Government also funded four return flights to New Zealand for Dame Goddard and her husband.
In accepting the resignation, the Home Secretary said the inquiry had "already instituted and made progress on its three core projects: the Research Project, the Truth Project; and the Public Hearings Project".
She thanked the judge for "bringing your experience to bear" and for 16 months of "commitment" and "hard work"