Philip, 96, was operated on earlier on Wednesday in a planned procedure after suffering with a hip problem for about a month.
The Queen, who is at Windsor Castle for the traditional Easter Court, is being kept fully informed about the condition of the duke, who was admitted to the private King Edward VII hospital in Marylebone, central London, on Tuesday.
Buckingham Palace said in a short statement: “The Duke of Edinburgh has undergone a successful hip replacement operation. He is progressing satisfactorily at this early stage.
“His Royal Highness is likely to remain in hospital for several days. He is comfortable and in good spirits.”
Details about which of the duke’s hip joints has been replaced have not been released by Buckingham Palace but the late Queen Mother underwent two successful hip operations in the 1990s, first when aged 95 then later when she was 97.