The sum Ms Geldof will receive has not been disclosed
Peaches Geldof, daughter of Bob Geldof, has accepted substantial, undisclosed libel damages over a newspaper claim that she had worked as a prostitute.
The 20-year-old brought proceedings to London's High Court over a story that appeared on the front page of The Daily Star in September, 2008.
The newspaper's solicitor Zoe Norden said her client accepted there was "no truth in the allegation".
She added that the paper apologised to the claimant "for any distress caused".
Ms Geldof's solicitor, Jonathan Coad, told Mr Justice Eady that the TV presenter had initially gone to the Press Complaints Commission over the front page spread.
He said that The Star's publishers, Express Newspapers, acknowledged the words used had implied she "provided services of a personal sexual nature for the payment of a fee".
Mr Coad added: "The defendant refused to publish a retraction and apology on its front page but instead published it on page two.
"As the publication was substantially smaller, the claimant considered this to be unacceptable as it was not, in her view, adequately prominent.
"The Press Complaints Commission adjudicated upon the prominence and found it to be proportionate.
"It is for this reason that the claimant now wishes to make this statement in open court to make the falsity of this allegation a matter of public record."
The sum of money that Ms Geldof will receive has not been disclosed, but the paper has also agreed to pay her legal costs.