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.
The 96-year-old Duke of Edinburgh was admitted to King Edward VII Hospital in Marylebone yesterday for the procedure.
Some media reports in the United Kingdom indicated that the timing of Prince Philip's hip replacement surgery was in preparation for the activities that will be involved in the royal wedding ceremony.
He was admitted on Tuesday to the King Edward VII Hospital in London which is regularly used by the royals. It is understood that the operation will require a general anaesthetic.
While Prince Philip has been in a fairly healthy condition throughout his life, he had been reportedly treated for a blocked coronary artery in 2011, and a bladder infection in 2012.
He did not accompany the Queen, 91, to a church service at a service last Thursday because of the hip problem, a royal source said last week.
"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".
Back in August 2017, the Duke retired from 65 decades of public service, significantly more than 5 decades after the Palace originally explained he would steadily "wind down" his workload, nevertheless he remained keen to carry out a number of his own obligations.
Prince Philip is in "good spirits" after having a hip replacement.
It was founded in 1899 at the suggestion of the then-Prince of Wales, and has treated most senior members of the royal family, including the Queen, Prince of Wales and the Duke of Cambridge. In 2016, he represented the royal family at 200 engagements.