"He is progressing satisfactorily at this early stage", the palace added in a statement Wednesday.
On Sunday the Duke was absent in an Easter service owned by the Queen and other members of the imperial family at St. George's Chapel in Windsoras well as the venue for Prince Harry and Meghanmarkle's Wedding Ceremony on May 1-9.
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.
Details about which of the duke's hip joints was replaced have not been released by Buckingham Palace.
The 96-year-old Duke of Edinburgh was admitted to King Edward VII Hospital in Marylebone yesterday for the procedure.
Buckingham Palace have confirmed that Prince Philip has been admitted to a London hospital for an operation on his hip, after missing a series of events. "He is comfortable and in good spirits".
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Scarlett McNally, an orthopaedic surgeon and council member of the Royal College of Surgeons, said fitness was more important than age when it came to recovering from surgery.
Philip was an avid sportsman for many years and saw active duty in the Royal Navy during World War II.
The Duke of Edinburgh pictured at King's Lynn railway station.
Prince Philip retired from 65 years of public service in August 2017, more than five years after the palace first said he would gradually "wind down" his workload, though he remained keen to carry out many of his duties.
They recently celebrated their 70th wedding anniversary.
In June 2013, Prince Philip reportedly spent 11 nights at a private London Clinic, following an abdominal surgery. Elizabeth, usually so guarded with her personal emotions, has publicly called him the rock that she depends on.