Philip joined the Queen at a luncheon for members of the Order of Merit.
The royal couple, who have just become great-grandparents for the eighth time following the arrival of Baby Sussex, posed for a group photograph at Windsor Castle in Berkshire.
The Queen was quizzed about the latest addition to the family by former Prime Minister of Canada, the Rt Hon Jean Chretien.
“Life is good for Your Majesty?” Mr Chretien asked.
The smiling Queen replied: “Yes, thank you”
“Congratulations. Another great-grandchild!” he added.
The Queen replied happily: “Yes, I know.”
She was then asked “How many of them have you got now?” before replying “Eight”.
Mr Chretien quipped: “You beat me by one.”
Buckingham Palace said on Monday that the Queen and the duke were “delighted” at the news of the birth of Harry and Meghan’s baby son.
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The Queen and Philip gathered with naturalist Sir David Attenborough, artist David Hockney, former Commons Speaker Baroness Boothroyd, and inventor of the World Wide Web Sir Timothy Berners-Lee, among others, for the picture.
The Order of Merit was created in 1902 by Edward VII to honour leaders in the arts, sciences, culture and military, and is limited to just 24 living members.
Philip, 97, was made a member of the Order in 1968.