But he found no evidence that decisions to limit its earlier inquiries into phone hacking were due to undue influence or corruption.
Leveson said senior police officers should ensure greater transparency over their meetings with the press in the future, and they should not be able to move immediately from the police into jobs in the media.
The Metropolitan Police said that the integrity of its officers had not been questioned but that it would study the criticisms made in the report.
Commissioner Bernard Hogan-Howe said he had already taken "decisive action" to address issues that emerged during the inquiry.
"Our priority now is the victims of phone hacking and making sure they get justice," he said.
Leveson described his inquiry, which heard from hundreds of witnesses during eight months of hearings, as "the most concentrated look at the press this country has ever seen."
Those testifying included politicians including Cameron and former Prime Ministers Tony Blair and Gordon Brown; police and media players such as Murdoch; and victims of press abuses.
The inquiry was first announced by Cameron in July 2011 in response to public outrage over a newspaper phone-hacking scandal.
The trigger was the allegation that in 2002, the voice mail of a missing 13-year-old girl, Milly Dowler, had been hacked by an investigator working for the News of the World newspaper before she was found murdered. Compounding the anger was the claim (later dismissed by police) that messages were deleted by him from the schoolgirl's full voice mail box, giving her parents false hope that she was alive.
The furor forced the closure of the 168-year-old News of the World, owned by News International.
It also prompted a new appetite among Britain's public and political establishments to see the sleazy underbelly of (often tabloid) reporting exposed and steps taken to clean up the media's act.
Leveson's report was the subject of much speculation before its release. Freedom of expression groups warned of a potential impacts on freedom of speech, while campaigners for greater controls said regulation is essential.
The chairman of the Press Complaints Commission, David Hunt, said he did not agree with all Leveson's recommendations but all those involved must seek to unite around "common ground."
"We all agree that we must regain the trust and confidence of the British people to make sure that unacceptable, outrageous and illegal behavior can never be allowed to happen again," Hunt said in a written statement.
The Committee to Protect Journalists issued a release saying it is "deeply concerned" about the recommendations.
"A media regulatory body anchored by statute cannot be described as voluntary," the committee's executive director, Joel Simon, said in the release. "Moreover, adopting statutory regulation would undermine press freedom in the UK and give legitimacy to governments around the world that routinely silence journalists through such controls."
Index on Censorship, a free speech group, urged "serious, considered debate" about the points made by Leveson.
Chief executive Kirsty Hughes said: "We share David Cameron's concerns that statutory underpinning would undermine free speech, and could be the start of a slippery slope of government interference in the media."
Media reform campaign group Hacked Off launched an online petition that calls on the leaders of the three main parties to implement the Leveson Report's recommendations in full "as soon as possible."
The actions of staffers at News Corp. and News International came under close scrutiny during the inquiry.
Among those to testify were Murdoch protege Rebekah Brooks, former chief executive of News International and onetime editor of the Sun and News of the World, and Andy Coulson, who also edited the News of the World. He went on to become Cameron's director of communications before resigning from that post early last year.
Both appeared in court Thursday morning to face charges of conspiracy to commit misconduct in a public office in connection with alleged illegal payments to public officials. They and three other accused were released on bail and ordered to appear in court again next week.
The scandal has also raised the specter of possible legal action against News Corp. staffers in the United States under the Foreign Corrupt Practices Act, which outlaws the bribery of foreign officials by U.S. firms.
However, analyst Porter Bibb in New York said the release of the Leveson report is "a nonevent" from the point of view of U.S. investors and would have no real impact on News Corp. stocks.
The corporation is doing well and Murdoch has come back "stronger than ever" following the pressure he was under to cede control of parts of his media empire early this year, Bibb said.