The picture, taken at Kensington Palace ahead of his birthday on Saturday, captures a smiling future king.
The Duke and Duchess of Cambridge were "delighted" to share the photograph taken by royal photographer Chris Jackson, Kensington Palace said.
The prince has spent the run-up to his birthday on a tour of Poland and Germany with his parents.
Prince George Alexander Louis - known as His Royal Highness Prince George of Cambridge - was born on 22 July 2013.