"I know that both of us will miss it terribly when my search and rescue tour of duty comes to an end next month and we have to move elsewhere," the Duke said.
"From the bottom of my heart, thank you for making my wife and me so welcome when we arrived here, as you do thousands of visitors each year.
"This island had been our first home together, and it will always be an immensely special place for us both."
The new father has been stationed as a pilot at RAF Valley at Anglesey since 2009. It is largely thought that he will return to London to join his regiment, the Household Cavalry's Blues and Royals, and care for his new family there.