The Sunday tabloid published the article in print and on the newspaper's website in January under the headline "Kate in Cocaine Coma". The story alleged that during a visit to Barcelona, Moss had collapsed into a drug-induced coma and had to be revived after taking large amounts of the class A drug cocaine.
The supermodel was not present at the settlement hearing at the High Court in London, where Moss's lawyer, Gerard Tyrrell, said the allegations were untrue.
Miror Group Newspapers, the national newspaper arm of Trinity Mirror, accepted that the allegations were false and agreed to pay the model damages, though the exact figure is not known.
Philip Conway, the Sunday Mirror's lawyer admitted the claims made were false and apologised.
Moss, 31, has been a model since she was 14 and has appeared in hundreds of advertising campaigns, most recently for beauty brand Rimmel and the Burberry Group.
She is currently in an on-off relationship with Pete Doherty, the former Libertines and Babyshambles singer, although news reports this week say that Moss has ended the turbulent relationship.
Some of the allegations were repeated in a Five show about Moss called 'The Truth about Kate Moss' and the channel is now waiting to see whether it will face legal action.
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