The apology came after Prince Philip used the landmark ruling in the Max Mosley sex case to try to protect the privacy of members of the Royal family.
In it's apology, the Evening Standard acknowledged that the allegation was not true adding that it was sorry for breaching his privacy, and for any distress the article may have caused the Royal Family.
The front page of August 9 newspaper says: "The Evening Standard apologises to the Duke of Edinburgh".
The full apology, which is published in an agreed position on page 5, says:
"HRH: The Duke of Edinburgh: Apology
"In the Evening Standard of 6 August we stated that The Duke of Edinburgh had been diagnosed as suffering from cancer of the prostate. We now accept that the story was untrue and that he is not suffering from any such condition.
"We unreservedly apologise both to him and to his family for making this distressing allegation and for breaching his privacy."
It was only after Buckingham Palace lodged a formal complaint that the Press Complaints Commission negotiated the apology, reports The Daily Telegraph.
Prince Philip is the first member of the Royal Family to have a complaint upheld over a breach of privacy, and the Queen and other members of the Royal family such as Prince William and Prince Harry have taken a close interest in the outcome of the complaint.
"We welcome this decision. We made two complaints: about accuracy because it was not true and about a breach of privacy. We are glad both were upheld so swiftly. This is a very significant ruling," a Buckingham Palace spokeswoman said.