The Charlie's Angels beauty has accepted "substantial" damages from The Sun's publisher, News Group Newspapers, over the story written in May.
But, following an investigation, the newspaper admitted in a statement: "Any suggestion of a romantic involvement is entirely untrue and without any substance whatsoever."
Diaz's lawyer Simon Smith told London's High Court, "It was explained to the reader that he was a married man, married to a high school teacher and that he was also the father of a one-year-old daughter," and that, "they have enjoyed more than just a professional relationship."
He continued, "The publication of these allegations has caused damage to the claimant's personal and professional reputation, in addition to obvious distress to both herself, Mr. Timberlake, Mr. Nickerson and his wife."
News Group Newspapers have settled a financial settlement with Diaz and agreed to cover her legal costs.
Smith added, "In those circumstances and in light of this vindication my client is prepared not to proceed any further against The Sun newspaper."
News Group Newspapers lawyer Benjamin Beabey argued his client's story was based upon an earlier report in The National Enquirer but added, "It entirely accepts that the allegations are without foundation and ought never to have been published."
Diaz is pursuing a separate legal action against American Media Inc.
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