Harry said: "Everyone says that babies change so much over two weeks we're basically monitoring how the changing process happens over this next month really. But his looks are changing every single day, so who knows."
Harry said he was looking forward to spending some "precious times with him as he slowly, slowly starts to grow up," before revealing the new addition to the family has already met his great-grandad the Duke of Edinburgh.
Meghan said: "We just bumped into the Duke as we were walking by which was so nice. So it'll be a nice moment to introduce the baby to more family and my mum's with us as well."
Asked to show more of their son's face to the cameras, Meghan laughed as Harry joked: "He's already got a little bit of facial hair as well, wonderful."
Meghan said: "Thank you everybody for all the well wishes and kindness, it just means so much."
There is still no sign of a baby name just yet, however the bookmakers favourites are Arthur with odds of 5-1, according to bookmakers Coral, while predictions for names such as Alexandra and Oliver have surged in popularity.