The article, published in the Daily Mail on 30 May 2009, was called "Who's Calling Parkies?" It alleged that Parkinson had acted in a "grossly insensitive" way toward his uncle, Bernard Parkinson, and that he had lied about his family upbringing in his autobiography.
The Daily Mail has accepted that the accusations were "entirely false."
Parkinson, 74, said he thought the Daily Mail had been delayed in publicly accepting their mistake.
"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," he said. ""In this case, it should not have taken nine months nor been so difficult for the editor to apologise promptly."
Parkinson said he would donate the damages to the Alexander Devine Children Cancer Trust and an unnamed school for orphans in South Africa.