The apology comes as part of a settlement between Ms. Miller and the newspaper, which also agreed to pay her £100,000 in legal fees and damages, about $164,000. It is the latest development in a long-running drama in which the newspaper has had to contend with growing evidence that its practice of hacking into the cellphones of public figures, politicians and celebrities was widespread and pervasive.
At least four other people who say their phones were hacked into have reached out-of-court settlements with the newspaper; numerous lawsuits against it are still pending. The newspaper has offered to settle with at least seven other possible victims of its phone-hacking practices.
For several years, News of the World said that its phone hacking had been limited to a single case — that involving its former royals editor, Clive Goodman, and a private investigator hired by the paper, Glenn Mulcaire, both jailed in 2007 for illegally intercepting voice mail messages of members of the royal household. But that claim began to lose credibility as more evidence came to light, and this year the company admitted that it had hacked the phones of eight public figures, including Ms. Miller, in the mid-2000s.
Meanwhile, the police are conducting a criminal investigation. Two News of the World editors and a reporter have been arrested in connection with the case.
The apology, read aloud in London’s High Court by a lawyer for News Group Newspapers, the subsidiary of Rupert Murdoch’s News International that publishes the News of the World, was notable for how thorough, and how abject, it was.
The company, said the lawyer, Michael Silverleaf, “acknowledges that the information should never have been obtained in the manner it was” and that “the private information should never have been published.” The paper, he added, “has accepted responsibility for misuse of private information, breach of confidence and harassment.”
Ms. Miller was not in court and did not make a statement. But her lawyer, David Sherborne, said that in 2005 and 2006, the News of the World published articles containing “intrusive and private information” about her.
She did not know “whether someone close to her was leaking information or whether her mobile telephone was somehow being hacked into,” Mr. Sherborne said. “Both possibilities were extremely distressing.”
He said that she had become suspicious about the security of her cellphone when she missed a number of voice mail messages and received calls from people who hung up.
The information was used for at least 11 articles about Ms. Miller’s private life, including details about her relationships with the actors Daniel Craig and Jude Law. One article drew on discussions between Mr. Law and Ms. Miller about the possibility of their having children together. The two have since split up.
News Group said that it would lay out the full extent of its phone-hacking operation to Ms. Miller privately.
Her case relied on notes, seized from Mr. Mulcaire after his arrest, with details about Ms. Miller’s cellphones, including phone numbers, PINs and passwords, as well as similar details about the phones of her mother, her publicist and Mr. Law.