Moss's lawyer Gerald Tyrrell told London's High Court that the model had accepted a public apology and a substantial but undisclosed sum from the Sunday Mirror over its report from January 23 this year.
The paper's article, headlined "Kate in Cocaine Coma" and tagged a "showbiz exclusive," had made a number of serious and defamatory allegations, he said.
The story had alleged that Moss, 31, had "collapsed into a drug induced coma and had to be revived after taking vast quantities of cocaine" in Barcelona in June 2001.
"These allegations are untrue," Tyrrell said.
The Sunday Mirror publishers now accepted that Moss had not behaved in this way and accepted that the allegations were false, he added.
The paper's lawyer Philip Conway told the court: "The defendant apologizes to Miss Moss for the distress and embarrassment they have caused her."