The Duke had been rushed to hospital from Balmoral Castle following a flare up of the bladder infection he suffered in June.
It is understood that the Duke, 91, is being treated with antibiotics to fight the infection in a private room inside the main NHS hospital, where he is expected to remain for the next few days.
A spokesman for Buckingham Palace announced shortly before 4pm yesterday: “The Duke of Edinburgh is responding well to treatment.
“It is unclear when he will be discharged, but he is likely to remain in hospital for a few more days.”
The brief statement from the palace followed a day of intense speculation about the health of the Duke, who has now been taken to hospital on three occasions within the past eight months.
A spokesman for NHS Grampian said: “No other patients have been clinically affected by the Duke of Edinburgh’s admission.”