The newspaper said in a court statement that it accepts the claims were without foundation and has offered an apology for two articles, published on January 29 and February 12 this year that alleged Weber had had a relationship with Benatti.
Mark Thomson, Weber's solicitor, said: "The defendant now accepts that the allegation is untrue. Not surprisingly, Ms Weber found the publication of the allegation very upsetting, especially since she was not asked about it prior to publication."
Thomson said that The Sunday Times had offered an apology and agreed to pay damages, which would include her legal costs, although a figure has not been disclosed.
Gillian Phillips, the Sunday Times' solicitor, said: "The defendant offers its sincere apologies to Ms Weber for publication of the defamatory allegations in The Sunday Times, which it accepts is untrue."
The stories came after Benatti was found to be in breach of his contract with WPP in March and ordered to pay €206,582 in damages, following his involvement in, and subsequent commission received for, advising on WPP's acquisition of Mediaclub for £14m in 2003, despite him owning a stake in the business.
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