Former deputy prime minister John Prescott and ex-minister Chris Bryant were also among the claimants whose settlements were confirmed by their lawyers at the High Court in London.
Lawyers for the claimants said the majority of people pursuing damages claims had now settled but that others would press ahead with a trial scheduled for next month.
Other settlements confirmed Thursday were Jude Law’s ex-wife Sadie Frost, Chelsea Premier League footballer Ashley Cole and Australian singer Dannii Minogue.
The size of the settlements was not immediately disclosed.
News Group Newspapers, the British publisher of the News of the World, has already settled dozens of compensation claims, including with British actress Sienna Miller, Law’s ex-girlfriend.
It has has set up a compensation scheme for victims of phone hacking in a bid to avoid further costly civil lawsuits.
Police said last year that they believe about 800 people had their voicemail hacked into by the News of the World, which Murdoch shut down in July as the hacking scandal spiralled.
There was no immediate comment from News International, the parent company of News Group.