"Mums and dads, aunts and uncles," she started by saying before adding with a knowing look and pointing to the camera: "Granny and grandpa!"
WATCH: Sarah Ferguson Gives Shout Out To 'Grandpa' Prince Andrew
The Duchess, wearing a printed dress and a floral hair garland, read The Unicorn and the Lost Cat by Claire Philip, as part of her daily videos for children.
Sarah made her first appearance on Wednesday after the birth of her grandson, appearing in a video where she made unicorn magnets.
Princess Eugenie and Jack Brooksbank's first child, whose name is still to be announced, arrived on Tuesday.
The first photo of Eugenie and Jack's baby son
In a statement, Buckingham Palace said: "Her Royal Highness Princess Eugenie was safely delivered of a son today, 9th February 2021, at 0855hrs at The Portland Hospital. Jack Brooksbank was present. The baby weighs 8lbs 1oz.
"This is Princess Eugenie and Jack Brooksbank's first child, The Duke of York and Sarah, Duchess of York's first grandchild, and the ninth great-grandchild for The Queen and The Duke of Edinburgh. Her Royal Highness and her child are both doing well."
The tot is 11th-in-line to throne behind his mother Eugenie, and will grow up without a title as titles are only passed down through the male line.
Eugenie shared the first photo of her baby son on Instagram on Tuesday – a sweet black and white shot of the proud parents holding the newborn's tiny fingers.
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