Mr Law had his phone hacked in the United States, the court heard, which opened the prospect of actions against the US parent company News Corporation, something the firm has been keen to avoid.
Mr Law accepted a settlement of £130,000 after he said his phone was hacked repeatedly, including at New York's JFK airport.
He told the court in a statement that "no aspect of my private life was safe from the News of the World".
Lord Prescott, the former deputy prime minister, and the Labour MP Chris Bryant are among 19 claimants whose settlements were also confirmed.
Other claimants who have settled include Shaun Russell, whose wife and daughter were killed in Kent in 1996, James Hewitt, the former cavalry officer, George Galloway, the former MP, and Gavin Henson, the Welsh rugby player.
Also among the settlements confirmed in court were Sara Payne, the mother of murdered schoolgirl Sarah, Sadie Frost, the actress, Ashley Cole, the footballer, Dannii Minogue, the singer, and Meg Matthews, the ex-wife of former Oasis guitarist Noel Gallagher.
The court heard that the number of phone hacking cases settled by the company now stood at 36.
Others such as former Labour Cabinet members David Blunkett and Tessa Jowell have also said that they have reached settlements, although News International would not confirm this.
It was said in other High Court proceedings in December, involving private investigator Glenn Mulcaire and NGN, that, as of then, more than 60 claimants had commenced proceedings against NGN and Mulcaire for breach of confidence and misuse of private information, with the majority outstanding.