Kate and Gerry McCann accepted £550,000 libel damages today over allegations that they were responsible for the death of their daughter Madeleine.
The couple, who were not at London's High Court for the hearing, said they were pleased Express Newspapers had admitted the "utter falsity" of the articles.
As well as the damages, the couple also accepted a public apology.
Their solicitor-advocate, Adam Tudor, told Mr Justice Eady that from the late summer of last year until February this year, the Daily Express, the Sunday Express, the Daily Star and the Daily Star Sunday, which have a combined circulation of several million copies as well as a substantial online readership, published more than 100 articles which were seriously defamatory of the couple.
He said: "The general theme of the articles was to suggest that Mr and Mrs McCann were responsible for the death of Madeleine or that there were strong or reasonable grounds for so suspecting and that they had then disposed of her body; and that they had then conspired to cover up their actions, including by creating 'diversions' to divert the police's attention away from evidence which would expose their guilt.
"Many of these articles were published on the front pages of the newspapers and on their websites, accompanied by sensational headlines.
"In addition to the allegations referred to above, the Daily Star published further articles (under the headlines 'Maddie mum 'sold' her' and 'Maddie 'sold' by hard-up McCanns') which sought to allege that Mr and Mrs McCann had sold their daughter in order to ease their financial burdens.
"A further article alleged that Mr and Mrs McCann were involved in 'swinging' or wife-swapping orgies."
Mr Tudor said that all the libel damages would be donated to the fund established to assist with the search for the four-year-old, who disappeared from Praia da Luz, Portugal, in May last year.
The Daily Express and Daily Star ran prominent pieces at the top of their front pages today, headlined "Kate and Gerry McCann: Sorry".
The McCann's lawyers complained several weeks ago over the articles, which appeared after Portuguese detectives last September named the couple as "arguidos", or official suspects, in their daughter's disappearance.
The McCanns are reserving the right to sue other papers for libel.
Last August they launched a defamation action against the Portuguese newspaper Tal & Qual over a front-page story which claimed police believed they killed their daughter.
The 24 August article alleged the Policia Judiciaria (PJ) - Portugal's CID - were certain the couple accidentally caused Madeleine's death.
It is understood that Tal & Qual has since folded.