The cards were sent to all members of the public who included their address along with their message of congratulations on the royal birth last month.
The message in the card reads: "The Duke and Duchess of Cambridge were most touched that you took the trouble to write as you did on the occasion of the birth of their son Prince George."
"Their Royal Highnesses have been overwhelmed by all the wonderful messages they have received and send you their warmest thanks and best wishes."
Prince George is also in the image, wrapped up in a bird print blanket.
The trio are standing outside the Lindo Wing at St Mary's Hospital in London, where George was born on July 22.
"The Duke and Duchess of Cambridge are very grateful for the support and goodwill being expressed at this happy time and wanted to acknowledge the letters and gifts they have received," a Kensington Palace spokesperson said.
Meanwhile, it emerged that the royal couple had saved the top three levels of their wedding cake for themselves, indicating they may be planning two more children.
The royal cake was a major creation featuring 900 sugar-paste flowers, and took a team of chefs five weeks to make for the wedding on April 29, 2011.
