Lord Mayor of London Fiona Woolf has replaced Lady Butler-Sloss as head of the UK government inquiry into historical child abuse.
Ms Woolf is a City lawyer and former president of the Law Society.
She will head an inquiry panel including child abuse experts and at least one victim of abuse.
Retired judge Baroness Butler-Sloss quit as head of the inquiry in July, saying she was "not the right person" for the job.
She stood down after child abuse victims raised concerns that she is the sister of the late Sir Michael Havers, who was attorney-general in the 1980s when abuse is alleged to have happened.
The inquiry, which was set up in July, was prompted by allegations that figures in Westminster and Whitehall were implicated in covering up child sex abuse, and that police and other authorities did not properly investigate prominent offenders such as Jimmy Savile and Cyril Smith.
Announcing Ms Woolf's appointment, Home Secretary Theresa May said: "In recent years, we have seen appalling cases of organised and persistent child sex abuse which have exposed serious failings by public bodies and important institutions.
"These failings have sent shockwaves through the country and shaken public confidence in the pillars of society in which we should have total trust.
"That is why the government has announced that an independent panel of experts will consider whether such organisations have taken seriously their duty of care to protect children from sexual abuse.
"We are absolutely clear that we must learn the lessons of past failures and the panel will be instrumental in helping us to do this."
Labour's shadow home secretary Yvette Cooper welcomed the fact that the inquiry was "finally moving forward".
But she added: "We still have no terms of reference for the inquiry and have had no assurances that it will look into current gaps that exist in the child protection system, as well as historical institutional failure.
"We now need urgent answers on both these issues."
Ms Woolf, 66, is an expert in energy markets and has advised many governments and the World Bank on privatisation and energy reforms.
'No time to lose'
As the Lord Mayor of London, she acts as ambassador for the City of London and Britain's financial services industry around the world.
She said: "Ensuring lessons are learned from the mistakes which have been made in the past and resulted in children being subjected to the most horrific crimes is a vital and solemn undertaking.
"I was honoured to be approached to lead such an important inquiry and look forward to working with the panel to ensure these mistakes are identified and never repeated."
She will be assisted as head of the inquiry by Graham Wilmer, a child sexual abuse victim and founder of the Lantern Project, which helps victims of sex abuse, and Barbara Hearn, former deputy chief executive of the National Children's Bureau.
Prof Alexis Jay, author of the recent report into abuse in Rotherham, will act as an expert adviser to the panel, said the Home Office.
Their first tasks are to finalise membership of the panel and agree terms of reference for the inquiry, said the Home Office in a statement.
Rochdale MP Simon Danczuk, who led calls for an overarching inquiry into alleged abuse, backed the appointment of Ms Woolf but called on her to bring "a sense of urgency" to the investigation.
He said the inquiry had lost momentum due to delays after the resignation of Lady Butler-Sloss.
"I'm pleased the Home Secretary has finally got this moving," said the Labour MP.
"Although I would not have looked to high office in the Square Mile to find someone to challenge the establishment, Fiona Woolf is a smart and capable woman and she has my support.
"Britain is in the middle of a child abuse crisis and this inquiry has to be a watershed. It must go to the heart of the establishment and challenge why crimes have been swept under the carpet for so long."
Mr Danczuk added that there was "no time to lose", as some alleged abusers were now very elderly and could die before facing justice.
Matthew Reed, chief executive of the Children's Society, echoed Mr Danczuk's call for no further delays to the inquiry but said it must be "thorough and comprehensive" and the voices of victims must be heard.
"This is a critical opportunity to eliminate the obstacles that have denied these children justice in the past and to stop this horrific crime from happening again," he added.