Trinity Mirror, which also owns the Sunday People, made the apology at the top of page two in today's Mirror, admitting that its hacking was "unlawful and never should have happened".
Last month, the High Court was told singer Cilla Black was among the latest group of celebrities to settle phone hacking damages claims for ''substantial'' damages.
EastEnders star Jessie Wallace, singer and TV personality Peter Andre and actor and singer Darren Day also settled actions against Trinity Mirror, which hasn't ruled out further costly allegations.
The apology admitted that Trinity Mirror unlawfully accessed information from private voicemails which was "used in stories in our national newspapers", adding that the practice had "long since been banished".
The Mirror apology reads in full:
Trinity Mirror, owner of the Daily Mirror, Sunday Mirror and Sunday People, today apologises publicly to all its victims of phone hacking.
Some years ago voice-mails left on certain people’s phones were unlawfully accessed. And in many cases the information obtained was used in stories in our national newspapers.
Such behaviour represented an unwarranted and unacceptable intrusion into people’s private lives.
It was unlawful and should never have happened, and fell far below the standards our readers expect and deserve.
We are taking this opportunity to give every victim a sincere and unreserved apology for what happened.
We recognise that our actions will have caused them distress for which we are truly sorry.
Our newspapers have a long and proud history of holding those in power to account. As such, it is only right we are held to account ourselves.
Such behaviour has long since been banished from Trinity Mirror’s business and we are committed to ensuring it will not happen again.
The cost of resolving claims will be "higher than previously envisaged", according to a trading update, and the company is increasing the provision for claims by £8 million to £12 million.
The update adds: "Inevitably there remains some uncertainty as to how matters will progress and whether or not new allegations or claims will emerge and their possible financial impact."
At a High Court hearing last month, barrister David Sherborne, representing the celebrities, read out statements on behalf of Ms Black and Mr Willis, Mr Andre, Mr Day and Ms Wallace, and also a further five in the cases of other individuals whose settlements have previously been reported, including former England football head coach Sven-Goran Eriksson, actor Christopher Eccleston and David and Victoria Beckham's former nanny Abbie Gibson.
It has been previously reported that Mr Eriksson and Mr Eccleston settled for £30,000 each and Ms Gibson for £15,000. It is understood from a court document that Mr Day was to receive £85,000 in damages.
Meanwhile, eight representative cases, none of which have been settled, are due to come before Mr Justice Mann in London on March 2.
They concern TV executive Alan Yentob, actress Sadie Frost, ex-footballer Paul Gascoigne, soap stars Lucy Taggart, Shane Richie and Shobna Gulati, flight attendant Lauren Alcorn and TV producer Robert Ashworth.
The two-week trial will determine the extent of the phone hacking and the amount of damages due.
Mr Sherborne said that, out of the outstanding claims, MGN had recently settled actions brought by fund manager Nicola Horlick for £25,000, model Emma Noble for £40,000 and stuntman Bobby Holland Hanton for £75,000.
The remaining live claims included those brought by Gascoigne's former wife Sheryl, actor John Thomson and TV presenter Davina McCall, with a number of others having been issued.
Scores of people, including high-profile celebrities, have reached similar settlements with the publisher of the now-defunct News Of The World newspaper after taking legal action in the wake of phone-hacking revelations.