Claims against News Group Newspapers by ex-Spice Girl Melanie C and actor Keith Allen were also settled.
The publisher of the Sun and the News of the World has agreed a “six figure” settlement to a phone-hacking claim from a former government minister.
Chris Huhne accused News Group Newspapers of “knowingly orchestrating unlawful information gathering in the UK” at executive level.
On Tuesday, the company apologised for the “behaviour of individuals working for or on behalf of the News of the World” but made no further admissions.
NGN also settled 11 other cases.
These included claims from the former Spice Girl Melanie Chisholm, and actors Keith Allen, Catherine Tate and Matthew Horne.
The News of the World closed suddenly in July 2011 as the phone-hacking scandal broke.
More than a decade on, dozens of cases are still being considered by the civil courts.
Chris Huhne was the Liberal Democrats’ shadow home secretary in 2009 and entered government as energy and climate change secretary when the party formed a coalition government with the Conservatives in 2010.
At court on Tuesday, he said he had agreed a “six figure sum” in damages with News Corporation’s legal entity News Group Newspapers and the company would pay his legal costs.
He accused News Corporation’s legal entity News Group Newspapers of hacking his phone as part of an attempt to obtain embarrassing material about him and remove him as a political opponent.
In 2009, Mr Huhne called for the expansion of a police investigation into phone hacking by people working for the newspaper.
He also opposed News Corporation’s bid at the time for UK satellite broadcaster BSkyB.
He said he believed the settlement “vindicates my long-standing claim that News Corporation directors and managers targeted me to get rid of a political opponent.”
“My case is unprecedented because the unlawful information gathering was directed not by journalists but by News Corp executives,” he said.
“They had two objectives: corporate espionage to help Murdoch’s bid for Sky, and bull-dozing pesky politicians out of the way.
He called on the Metropolitan Police to open a new investigation into directors and managers at News Corporation.
News Group Newspapers made no apology to Mr Huhne, in contrast to its legal response to other cases it had settled. A legal response contained no admissions relating to the former politician’s allegations.
Mr Huhne said he had not requested a court apology but had settled because he would not achieve a bigger damages pay-out by going to trial.