The couple's action against the News of the World was due to be tried at London's High Court in December. However, it was delayed until after the World Cup in June, in which 30-year-old Beckham will captain England.
In a brief statement issued yesterday, the couple's spokeswoman, Jo Milloy, said the action had been resolved "on a confidential basis".
Details of the case over a 2004 article entitled "Posh and Becks on Rocks" were revealed in October during pre-trial applications for disclosure of documents.
Mr Justice Gray heard that the Beckhams' case was that the article implied they were cynically trying to convince the public that their failed marriage was perfect to protect their image and for financial reasons.
They also claimed the story suggested the couple's rows had brought David Beckham to the edge of a nervous breakdown and threatened his wife's health during pregnancy.
The Beckhams said there was no truth in the claims.
Richard Spearman QC, for the News of the World, said the defence would be justification on the grounds that the article was true.
He said: "Because their substantial fortunes depend upon their public perception, the claimants have been cynically and hypocritically trying - for financial reasons - to convince the public that they continue to enjoy a happy marriage."
The judge was told the newspaper would allege David Beckham was unfaithful to his wife with his former personal assistant Rebecca Loos, a claim Beckham has denied.