He added: "I remain firmly of the belief that the British press - I repeat, all of it - serves the country very well for the vast majority of the time."
He singled out The Daily Telegraph's investigations into MPs' expenses, the Daily Mail's campaign to bring the killers of Stephen Lawrence to justice and the Sunday Times's exposure of the effects of thalidomide as the "best known" examples of "great journalism, great investigations and great campaigns".
On too many occasions, however, such as in the hacking of the mobile phone of the murdered schoolgirl Milly Dowler, which prompted the Leveson Inquiry, the press had treated the rights of ordinary people with "disdain".
He said: "There must be change. But let me say this very clearly. Not a single witness proposed that either Government or politicians all of whom the press hold to account, should be involved in the regulation of the press. Neither would I make any such proposal."
The High Court judge insisted that a new independent regulator, with the power to fine newspapers up to £1 million, could only work if it was underpinned by legislation, otherwise publishers might simply opt out.
He said the press should decide how the new watchdog should work, with a legal framework "to support press freedom, provide stability and guarantee for the public that this new body is independent and effective".
He added: "This is not, and cannot reasonably or fairly be characterised as statutory regulation of the press."
He pointed out that his Inquiry was the seventh time in less than 70 years that such issues had been addressed.
"No-one can think it makes any sense to contemplate an eighth," he added.
In his 1,987-page report he suggests an independent regulator with the power to fine newspapers up to £1m or 1 per cent of turnover for breaching a new code of standards, and says it should be up to the media to agree the form and powers of the new watchdog.
The new body, he says, should have an arbitration system to enable wronged parties to seek swift redress by way of a prominent apology and fines, if appropriate.
The arbitration system would also help newspapers avoid costly libel action, he suggests, because litigants who refused to accept this "cheap route to justice" could be deprived of large damages or court costs if they took the matter to trial.
Lord Justice Leveson suggests a kite mark system for publications that are signed up to the new regulator and a whistleblowing hotline for journalists who believe they are being put under pressure to breach a new code of conduct, with legal protection to prevent them being victimised for doing so.
The broadcasting regulator Ofcom should carry out reviews every two years of how the new regulator is working, he suggests, and should act as a "backstop" regulator if publishers refuse to sign up to the new body.
The Information Commissioner should also be given greater powers to prosecute newspapers for breaches of data protection.
The board of the new regulatory body, says the Leveson Report, should comprise a majority of people independent of the press, with some former journalists but no serving editors and no MPs.
One of the most draconian measures proposed in the report is a suggestion that journalists should lose the right to withhold from the police documents given to them in confidence and notes and recordings of conversations with confidential sources.
Lord Justice Leveson recommends that journalistic material should only be exempt from legal proceedings when it is "subject to an enforceable or lawful undertaking", meaning in future journalists might have to sign contracts with any confidential sources to protect them.
The report also suggests changes in the way journalists interact with politicians and police officers.
Off the record briefings by police officers should be replaced with "non-reportable briefings" for background or "embargoed briefings" for use at a later date to avoid confusion, and senior officers should publish a list of all meetings with the media.
Members of the Government and the Opposition front benches should publish a list of meetings with editors, proprietors and media executives on a quarterly basis as well as a summary of their phone calls, text messages, emails and letters between them.
The recommendations of the Leveson Report are not binding and Lord Justice Leveson concluded: "The ball now moves back into the politicians' court: they must now decide who guards the guardians."