The photos show Prince George at the family’s Norfolk home, Anmer Hall, and were taken in mid-July by photographer Matt Porteous.
One of them shows him playing with the family dog Lupo.
Prince George Alexander Louis – aka His Royal Highness Prince George of Cambridge – was born on July 22 2013.
A Kensington Palace spokesman said: “The Duke and Duchess hope that people will enjoy seeing these new photographs.
“They would like to thank everyone for all the lovely messages they have received as Prince George celebrates his third birthday.”
However, the Royal Society for the Prevention of Cruelty to Animals (RSPCA) has criticized the picture of the little prince holding an ice cream close to the mouth of the family dog.
A RSPCA spokesman said: “It is lovely that Prince George is trying to help keep his family dog, Lupo, cool in these high temperatures.
“We would advise people to be cautious when giving their dogs food meant for human consumption as some items, like chocolate, can be highly toxic to dogs and dairy items can be difficult for them to digest.
“Instead of ice cream we would suggest making an ice lolly from pet-friendly ingredients. Making these can be really fun for children and the end product is both safe and enjoyable for dogs.”
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