The Prime Minister will give the go ahead for the ship to be commissioned within weeks, according to the Daily Telegraph.
Arguments between The Ministry of Defence and Cabinet Office over who should foot the bill for the ship are said to have delayed the announcement.
Conservative MP Craig Mackinlay, who has led a campaign for a successor to Britannia, said he was “overjoyed” at the news.
He told the Daily Telegraph: ““A new national flagship proudly bearing the name of Prince Philip can be no better memorial to this much-loved and respected man.
“I am delighted that the years of effort to prove to ministers the value of such a vessel to our country’s global brand is now on the brink of becoming reality.
Sir John justified his decision in an interview with the Daily Mail, saying: “During the early Nineties, the monarchy went through a very difficult time.
“Ask yourself this question: in the midst of the recession, with the British people facing economic hardship, how popular would it have been to announce a £50 million spend on a new yacht for the personal use of the Royal Family?
“How would that have been portrayed by the media?”