The agreement follows a similar deal with actress Sienna Miller last month, who dropped her civil case against NGN for £100,000 in damages.
In a statement, News International said: "News Group Newspapers announces today that it has reached an agreement with Andy Gray to pay him £20,000 in damages plus undisclosed costs.
"This concludes the action Andy Gray was taking against NGN over voicemail interception in relation to the News of the World."
Gray's case against the publisher was one of five due to be heard in January 2012, together with those brought by Jude Law, football agent Sky Andrew, politician Chris Bryant and interior designer Kelly Hoppen.
The Guardian reports that one of five reserve cases chosen by Justice Vos last month may now take the place of Gray's in the planned trial.
The reserve cases include those brought by politician and former Celebrity Big Brother star George Galloway, ex-England footballer Paul Gascoigne and actor Steve Coogan.
In April, the News of the World printed a formal apology over the phone hacking scandal.