News Group Newspapers offered payments to Coronation Street actor Jimmi Harkishin, TV presenter Kate Thornton, comedian Vic Reeves and former Spice Girls manager Chris Herbert.
The four claims were due to be heard at the High Court but were abandoned after payouts were offered.
The alleged victims said the papers gathered information unlawfully.
According to the claimants, journalists at the News of the World and the Sun used phone hacking and “blagging” – tricking businesses into releasing confidential information – to find stories about them.
The four claimants said this led to the publication of 79 articles that they disputed.
Reeves’ claim was made was under his real name of Jim Moir.
Destruction of emails
News Group Newspapers (NGN) has denied that phone hacking took place at The Sun and made no admissions in the latest settlement. But a total of 23 hacking claims against the newspaper group have now been settled.
Civil claims against NGN have been moving through the courts since 2012 and have resulted in four aborted trials, costing NGN millions in legal fees.
BBC home affairs producer Gaetan Portal, who was at the High Court, said that each of these latest cases incurred fees of about £450,000 to £500,000, on top of compensation believed to be a six-figure sum for each claim.
As well as the four named cases, the court was due to hear two “generic” claims involving phone hacking at The Sun and allegations that senior executives at NGN conspired to destroy documents, computer equipment and millions of emails.
It was alleged that James Murdoch, chairman of the company when it was known as News International, and chief executive Rebekah Brooks adopted a strategy to destroy materials in 2010 after they received court papers from lawyers representing the actress Sienna Miller.
The destruction of emails allegedly continued into 2011 as the Metropolitan Police began its investigation into phone hacking.
By BBC legal correspondent Clive Coleman
“It’s deja vu all over again” is a phrase attributed to the legendary American baseball coach Yogi Berra.
It might also describe today’s settlements.
For six years, News Group Newspapers has settled claims for phone-hacking before they came to trial.
Finally, the issue of whether the publisher is liable was due to be determined in a civil court with the cases due to start today… but it didn’t.
NGN has now settled around 1,000 civil claims for phone-hacking.
If the cost estimate for a single claimant of £450,000 to £500,0000 given in court is typical, then the publisher is likely to have paid in the region of half a billion pounds in costs alone.
Compensation payments would run into tens of millions more.
And there are scores more claims in the pipeline including from Sir Elton John and the actor David Tennant.
More concerning for NG though are the so-called ‘generic’ claims being brought by ‘various claimants’ alleging concealment and destruction of evidence by senior executives.
They are much more difficult to settle.
NGN has always maintained that emails were deleted as part of their normal IT systems management.
David Sherborne, representing the claimants, said they made serious allegations of criminality against James Murdoch and Rebekah Brooks over the destruction of material.
Mr Justice Mann criticised both parties for the way the cases had been handled. He said: “Settlement is a good thing… even at the court doors… however for test cases it raises different issues.”
He said that the cases had been a chance to settle the wider issues of whether there had been a “deliberate cover-up” and illegal activity at The Sun.