Murdoch's company previously paid millions of pounds in settlement to the family of murdered British teenager Milly Dowler.
The seven public figures whose claims have been settled include Princess Diana's former lover James Hewitt, former Liberal Democrat MP Mark Oaten, TV presenter Ulrika Jonsson, Abi Titmuss, Calum Best, ex-MP Michelle Milburn and Paul Dadge, who helped survivors of the London bombings. News International said it had agreed to pay "appropriate sums" to compensate them for the distress caused.
The settlement figures are expected to be in hundreds of thousands of pounds.
News of the latest settlement came amidst continuing inquiries into the phone-hacking row, including the Leveson inquiry, where celebrity journalist and television presenter Piers Morgan was due to appear via videolink from the US, where he works for the CNN.
Morgan, a former editor of the News of the World and Daily Mirror, wrote in his memoirs about unethical news gathering practices in tabloid newsrooms.
He is expected to be questioned at the Leveson inquiry on such references in his memoirs.
Morgan has recently denied ever hacking a phone or knowingly running a story based on hacked information.
In his memoir, he mentions a 2006 article in which he said he was played a phone message left by former Beatle Paul McCartney on the answering machine of his now ex-wife Heather Mills.
Mills has said there was no way Morgan could have gotten hold of the message honestly.