Judge Lowell Goddard issued a stark warning to individuals and institutions that they will face scrutiny “no matter how apparently powerful”.
She said both victims and society had been left “scarred” by historic abuse and referred to estimates suggesting that one in 20 children in the UK has fallen victim as evidence of the “sheer scale” of the problem.
Finally opening the troubled inquiry, the judge stressed it will not hesitate to make findings relating to named people and organisations.
The probe is expected to take up to five years and cost tens of millions of pounds.
All strands of public life in England and Wales will come under the spotlight - including politics, children’s homes, hospitals, GPs’ surgeries, schools, churches, charities, local authorities, the Crown Prosecution Service, the NHS, the BBC and the armed forces.
The panel will examine allegations of abuse by prominent figures, with this work including inquiries relating to individuals in central government, political parties, the security and intelligence services, as well as present and former members of the Special Branch.
It may also need to challenge “powerful private interests” such as internet service providers and insurance companies, Justice Goddard suggested.
She said: “We must travel from the corridors of power in Westminster to children’s homes in the poorest parts of the country.
“We must put difficult questions to politicians, bishops and other faith leaders, headteachers, police officers, regulators, inspectors and public officials of all kinds. And we will carry on putting those questions until we get answers.
“No-one, no matter how apparently powerful, will be allowed to obstruct our inquiries into institutional failings, and no-one will have immunity from scrutiny by virtue of their position.
“We have the tools we need to get at the truth and we will not hesitate to use them.”
The inquiry can compel witnesses to give evidence but is not able to determine criminal or civil liability.
Justice Goddard stressed that her panel will not hesitate to make “findings of fact” about alleged conduct in relation to named individuals or institutions “where the evidence justifies this”.
The New Zealand high court judge said “too many individuals and institutions” have been “sheltered from accountability through patterns of indifference or obstruction”.
She added: “It is a stark reality that some abusers have abused their positions of trust within institutions as a means of gaining unfettered access to children.”
The inquiry provides an opportunity to “expose past failures of institutions to protect children” and to “confront those responsible”, she added.
She issued a call for child abuse victims to come forward, as well as laying down a “challenge” to organisations with a duty of care to protect children, telling them: “I urge you to take a pro-active stance towards the inquiry ... rather than waiting for us to come and see you.”
The judge conceded that the task facing the five-person panel is “daunting”, saying: “This is the largest and most ambitious public inquiry ever established in England and Wales.”
She said she hopes their work will be completed by the end of 2020 and is determined that it is not “bogged down” by delays that have “bedevilled” other major probes.
Home Secretary Theresa May has approved a budget of £17.9 million for the operation of the inquiry over the coming year.
The chairwoman said tackling child abuse “cannot be calculated in monetary terms”, adding: “It is the inherent right of every child to experience a childhood free of sexual abuse and intimidation.”
Details of the inquiry revealed in the statement, delivered in Westminster, include:
• The terms of reference include all state and non-state institutions;
• Investigations have no cut-off date and may include events dating back decades;
• The inquiry’s work will be divided into five “workstreams” - allegations of abuse by those prominent in public life; education and religious settings; criminal justice and law enforcement; local authorities and voluntary organisations; and national and private service organisations;
• There will be three “core projects” - the research project; the truth project, in which victims and survivors’ accounts will be taken in private; and the public hearings project, in which a number of “paradigm cases” will be considered. Public hearings will not begin for several months;
• A wide range of institutions have been told to preserve all records relating to the care of children;
• Whistleblowers will be given legal protection from prosecution under the Official Secrets Act.
The inquiry - set up last July following claims of a high-level cover-up of abuse - has been beset by delays following the resignations of two previous chairwomen.