The Daily Mail had been serialising Sir Michael's autobiography
Broadcaster Sir Michael Parkinson has accepted £25,000 libel damages from the Daily Mail over an article claiming he had lied about his family background.
The article - Who's Telling Parkies, printed in May last year, suggested he had behaved in a grossly insensitive way towards his elderly uncle.
The 74-year-old, who was at London's High Court for the settlement, has agreed to donate his payout to charity.
The Daily Mail has now accepted the allegations were "entirely false".
In a statement, Sir Michael said: "As a journalist myself, I have been reluctant to take legal action against any newspaper.
"Where defamatory allegations have been published about me, I have always, until now, turned a blind eye."
He went on to say that he thought the paper had "crossed a line", particularly as it had been serialising his autobiography called Parky, My Autobiography.
"During my nearly 60 years as a journalist, I have always believed it was standard journalistic practice, as well as a matter of common decency, for a newspaper to apologise publicly and promptly when they have made a mistake.
"In this case, it should not have taken nine months nor been so difficult for the editor to apologise promptly.
"Moreover, I believe that the persistent delaying tactics of the Daily Mail were both unattractive and unworthy of a national newspaper.
"At a time when the media is seeking greater freedom, I think it is counterproductive for a newspaper to behave in this way."
Sir Michael's solicitor-advocate, Mark Thomson, told Mr Justice Eady that his client had never mistreated his uncle and did not lie about his background in order to charm readers.
In Wednesday's edition, the Daily Mail said: "An article of 30 May 2009 reported claims that Sir Michael had threatened to sue a relative over suggestions that the former chat show host had been insensitive to his uncle and had lied about his father in his autobiography.
"We accept that Sir Michael had not lied about his family or been insensitive. We apologise for any distress caused and have agreed to pay him damages and costs."