The couple were not present at London's High Court for the settlement
Sharon Osbourne has accepted libel damages from The Sun newspaper over a 2007 story which alleged she was driving husband Ozzy "to destruction".
The 56-year-old former X Factor judge accepted an apology and a substantial, undisclosed sum of money.
Her solicitor told the court that the allegations were "entirely without foundation" and "extremely distressing, hurtful and damaging".
The star was not at London's High Court for the settlement.
Solicitor John Kelly said the article, published in October 2007, claimed that Mrs Osbourne was "driving her frail husband Ozzy Osbourne to destruction" and was working him "so hard she will kill him".
It alleged that she was forcing the Black Sabbath star to perform in a series of live shows in order to fund her exorbitant spending.
The article continued: "Sharon will keep Ozzy on the road until, like Tommy Cooper, he dies on stage".
Mr Kelly said the publication had caused damage to his client's personal and professional reputation and she had suffered considerable embarrassment and distress.
Patrick Callaghan, solicitor for News Group Newspapers, said it sincerely apologised and accepted that the allegations were untrue and ought never to have been published.
In addition to the libel damages, the newspaper also agreed to pay Mrs Osbourne's costs.
A spokesman for the star said: "Sharon is delighted to have won her case. She would prefer not to have to take legal action against the media, but had no alternative in this case.
"Sharon and Ozzy are pleased that they can put this matter behind them," she added.
Last year, Ozzy Osbourne accepted libel damages from the Daily Star over allegations he suffered a health scare which jeopardised the 2008 Brit Awards, at which he was a co-host.
The article claimed Osbourne collapsed twice before the ceremony, implying that he was in such poor health that he was incapable of presenting.
Express Newspapers apologised and accepted the allegations were untrue and should not have been published.