The case was heard at the high court, centering on an article in the Daily Mail on 6 March. The story alleged that Kidman had led Law to cheat on his wife Sadie Frost, with the couple subsequently seperating.
The article further alleged that Kidman's denials of the affair were dishonest, and Gideon Benaim, solicitor for the actress, said: "The publication of this article has caused grave damage to the claimant's personal and professional reputation, and she has suffered considerable embarrassment and distress."
Kidman and Law had been shooting the film 'Cold Mountain' when rumours of the affair began to circulate.
The Daily Mail and parent company Associated Newspapers have agreed to pay damages and legal costs as part of the settlement, as well as making a formal apology. Kidman has sued two other newspapers that carried the story: the Sunday Telegraph, which apologised within a week; and the Sun, with the case yet to be resolved.
The Australian actress was once married to Tom Cruise, with whom she had two children. The couple were no strangers to libel action, with almost constant press speculation about their relationship during the 10 years they were together.
Various allegations that the couple have sued over include claims that Cruise is gay, and stories that the director Stanley Kubrick hired a sex therapist to advise them while filming the erotic thriller 'Eyes Wide Shut'.
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