@KensingtonRoyal, the official Twitter handle of The Duke and Duchess of Cambridge and the Royal Foundation based at Kensington Palace, posted the picture on Christmas, garnering 3,600 retweets and 44,500 likes.
"Merry Christmas to all our followers!
"This photograph of The Duke of Cambridge, Prince George, Princess Charlotte and Prince Louis was taken by The Duchess of Cambridge (Kate Middleton) in Norfolk earlier this year," read the accompanying message.
A gushing fan wrote: "My Christmas present; Thank you, I'm freaking out. OMG!"
"So glad your wish came true. It's such a lovely photo, isn't it?" remarked another fan.
One user wrote: "Thank you so much for making our Christmas 10000000000000000x better!!! I love this family!"
Another tweeted: "Thank you for this beautiful photo of a beautiful family. Merry Christmas!"
"I LOVE Y'ALL SO MUCH," read one tweet.
"Ohhh, what a fantastic picture!! The Duchess's passion for photography and love for her family are positively beaming from this image!!! Thank you so much for sharing it with us!! Happy Christmas to the Cambridge family and best wishes for the New Year!!!"
A post read: "Ok look, it's genuine! A great picture of a lovely family."
In the picture, Prince William wearing a flat cap is seen kissing Prince Louis on the cheek, even as Princess Charlotte appears to be holding on to her younger brother while Prince George sits next to them.
It is not the first time that Kate Middleton, one of the most photographed people in the world, has gone behind the camera and released her own pictures.
The Duchess was named as the new patron of the Royal Photographic Society this year following her passion for photography.
( With inputs from IANS )