The endeavour has been a political minefield. Home Secretary Theresa May said Justice Goddard had been selected after a search that involved more than 150 candidates, "due diligence" on potential conflicts and consultation with victim groups.
The existing panel is being dissolved, with members able to reapply for positions, Mrs May told MPs. The terms of reference are also being revisited, potentially meaning that investigations could go back beyond 1970.
Mrs May said she was "more determined than ever" to expose people and institutions who had failed victims.
"The Home Office received more than 150 nominations from survivors, their representatives, MPs and members of the public," she said. "In addition, the Home Office also contacted Commonwealth countries via the Foreign Office to identify any suitable candidates.
"Each and every name was assessed against a set of criteria incorporating the views of survivors on the most important factors.
"This included the appropriate skills to carry out this complex task, experience of that subject matter, and the absence of any direct links to any individual about whom people may have concerns, or any institution or organisation that might fall under the scope of the inquiry."
Labour MP Simon Danczuk, who has been campaigning on the child sex abuse issue, said the inquiry now appeared to be going in the "right direction".
"I welcome the appointment of Justice Lowell Goddard to chair the Child Abuse Inquiry," he said. "This has been a long and difficult process for survivors of abuse, and I know they will share my relief that we can finally get under way and that the Inquiry will begin before the general election.
"I had a productive meeting with the Home Secretary this morning, and I have confidence in the process she has gone through in order to find a new chair. It is obvious that the Home Secretary has cast the net far and wide in order to find an appropriate person and I applaud her for doing so.
"I particularly welcome the fact that the Inquiry will have the statutory powers that are needed and that I and others have been calling for. I also believe it is the right decision to reconstitute the panel and to broaden the terms of reference so that there is no cut-off date for evidence."
Justice Goddard is believed to be the first woman of Maori descent to have served as a High Court Judge.
Mrs May said she had met with many victims and their representatives since making her last statement to Parliament on the issue in November. "During those meeting, many people shared their experiences no matter how painful, no matter how difficult it was to speak out," she said.
"In doing so the young survivors displayed immense courage, as did the older survivors who showed me how abuse that took place decades ago can feel like it took place yesterday... I am grateful to all of them."
"Let me be clear. I am now more determined than ever to expose the people behind these despicable crimes and the people in institutions that knew about abuse but didn't act, that failed to help when it was their duty, sometimes their very purpose to do so. And the people and institutions that in some cases positively covered up evidence of abuse."
Mrs May conceded "not every survivor" would agree with what she had announced, but said there was a great deal of consensus on what was needed for the inquiry.
The first person appointed to lead the inquiry was Baroness Butler-Sloss, who stood down as chairwoman in July last year amid questions over the role played by her late brother, Lord Havers, who was attorney general in the 1980s.
Her replacement Dame Fiona Woolf resigned following a barrage of criticism over her "Establishment links", most notably in relation to former home secretary Leon Brittan, who died last month.