The 92-two-year duke had been in medical care since June 6.
The Guardian said Philip "walked out of the London Clinic, smiling and holding a large book."
Buckingham Palace earlier said the surgery was not an emergency operation, but Philip had been expected to stay under medical care for several weeks.
The palace said the duke will likely take several weeks to fully recover. Even so, he is said to be in good spirits.
The details regarding the duke's operation have not been made public. According to the Guardian, surgery was deemed necessary on the "basis of earlier abdominal investigations."