Buckingham Palace says the procedure for the Queen's 96-year-old husband had been planned.
The Duke of Edinburgh, 96, was admitted to the private King Edward VII Hospital in London yesterday.
Very last June, Prince Philip put in two nights in hospital as a "precautionary measure" to its treating an undisclosed infection.
Buckingham Palace said the surgery went well and that he is "progressing satisfactorily at this early stage" while staying in "good spirits", local news outlets reported.
He is said to be "comfortable and in good spirits". It is understood that the operation will require a general anaesthetic.
The duke retired from official duties a year ago.
Ex-spy poisoning row: Britain unable to identify source of nerve agent
Britain blames Russian Federation for the March 4 attack on Skripal and his daughter Yulia, a claim Moscow fiercely denies. Later, London claimed that the toxin of Novichok-class had been allegedly developed in Russian Federation .
Ananda Nanu, the board's president, said hip replacement patients need strong pain relief after their operations.
He has missed a series of engagements and events over the last month, including the recent Easter Sunday service at St. George's Chapel in Windsor.
"What is most important is someone's fitness, as in their heart and lung fitness, how much exercise they do and how well nourished they are".
Prince Philip had announced his retirement in May 2017, after decades of supporting the Queen as well as attending events for his own charities and organisations.
His final solo engagement was in August previous year, when he reviewed a parade of Royal Marines outside Buckingham Palace in his capacity as Captain General of the corps.
There's a busy few months coming up for the royal family, as the Duke and Cambridge prepare to welcome their third child, and Prince Harry and Meghan Markle marry next month. In 2016, he represented the royal family at 200 engagements.
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