According to the Press Complaints Commission, Allegra Versace Beck made a formal complaint through her solicitors after the celebrity magazine published an article and photos in September 2004 entitled "Yes, you can be too rich and too thin".
Ms Versace Beck, who inherited a 50% stake in the Versace designer empire on her 18th birthday, said that the article and photo intruded into her privacy.
This, she argued, breached a clause in the Commission's Code of Practice that says "Everyone is entitled to respect for his or her private and family life, home, health and correspondence, including digital communications. Editors will be expected to justify intrusions into any individual's private life without consent."
The complaint has been resolved with the magazine publishing an apology to Ms Versace Beck.
The magazine also undertook not to repeat the article, re-publish the photos or publish any further material on her private life, health or general well being unless authorised by her or her representatives.
The apology follows a landmark ruling by the European Court of Human Rights last year. It ruled that publishing paparazzi photographs of Princess Caroline of Monaco in a public place was a violation of her right to privacy.
On that occasion, the Court considered that the general public did not have a legitimate interest in knowing Caroline von Hannover's whereabouts or how she behaved generally in her private life even if she appeared in places that could not always be described as secluded and was well known to the public.
The Court reiterated the fundamental importance of protecting private life "from the point of view of the development of every human being's personality" and said that everyone, including people known to the public, had to have a "legitimate expectation" that his or her private life would be protected.