Lady Justice Hallett, who was appointed to conduct the review ordered by Prime Minister David Cameron, has been promised full co-operation and access to all relevant material by official departments and agencies.
She said: "I intend to conduct a full and rigorous examination of the administrative scheme from its inception to date. Although appointed by Government, I will carry out my task independently and impartially."
It comes after a row erupted last month when it emerged that the Westminster Government had sent letters to nearly 200 republicans saying they were no longer wanted.
Lady Hallett continued: "I have been promised full co-operation and access to all relevant material by the relevant government departments and agencies.
No individual or organisation is on trial.
Lady Justice Hallett
"However, I am seeking to establish the facts and, where necessary, accountability in relation to what happened, ie, how the scheme evolved and who was or is responsible for its operation."
It has also emerged that the PSNI will look into the process that led to the letters being sent.
A team of 16 detectives has been assigned to review the cases. They will investigate the circumstances of each of those who received a letter and also re-examine the original checks carried out by the PSNI. Cases may be reopened if mistakes or new evidence are uncovered.
Meanwhile a parliamentary debate over 'on-the-runs' has been taking place on Thursday.
Nigel Dodds, DUP MP for Belfast North, said former Northern Ireland secretary Peter Hain may have been economical with the truth when answering questions on this issue.
He told the Commons: "I think it would be important to hear in this House, on the record, from those previous ministers as to whether or not they stand over some of the statements that they made in this House, because when one reads them, it is very, very clear that there was certainly an economy when it came to the truthfulness of what was being said."
Mr Dodds referred to a question which he said was asked to Mr Hain by Peter Robinson DUP in 2006 about there being "no other procedure to allow the on the run terrorists to return".
He said: "The (then) secretary of state answered: 'There is no other procedure'."
This was done as a dirty deal behind the backs of everybody concerned.
Independent MP for North Down Lady Sylvia Hermon said it "is with considerable regret that Mr Hain is not here today" but added in his defence "that he was attending the funeral, quite properly, of his colleague and dear friend Tony Benn".
Alliance MP for Belfast East Naomi Long said the issue of OTR letters has "compounded" the feeling among loyalists that justice in Northern Ireland is biased against them.
She said: "That is the perception, I have to say, which I have not shared, but I am hugely aggrieved that, as a result of this, that perception has been compounded.
"Only members of Sinn Féin, who came through Sinn Féin, had access to this scheme.
"In fact there are complaints from other republicans who fell out of favour with the leadership that they weren't even able to access this scheme. So justice, in fact, in NI was acting in a partial way during that process and that has undermined confidence in the public.
"It has further damaged people's respect for the PSNI, who have been, by implication, asked to do this job by the government of the day and did it as they were asked to do and is their duty."
Details of letters sent to 'on-the-runs' detailing whether or not they were wanted by police for any crimes emerged in February when such a letter - sent in error - caused a trial to collapse.
John Downey, accused of carrying out the 1982 Hyde Park bombing which killed four soldiers, walked free from the Old Bailey because he had been assured that he was not a wanted man.
The 62-year-old from Co Donegal, who denied all charges against him, had received a letter in 2007.
This week it emerged through correspondence between the Northern Ireland Office and the Lord Chief Justice of England and Wales that the judge leading the independent inquiry into the letters scheme, Lady Justice Hallett, will not be examining each case.
However the DUP leader Peter Robinson said: "All of the cases will be reviewed, whether they are reviewed by the police or by the judge is the issue."
Meanwhile deputy First Minister Martin McGuinness has said that the letters remain lawful.
The Sinn Féin politician said: "There can't be any rescinding of an agreement which two governments effectively stood over and which Dominic Grieve, the Attorney General, said in the House of Commons was a perfectly lawful process."