She's believed to be suffering with acute morning sickness "Hyperemesis Gravidarium". She is being cared for at their London home.
An Australian Monarchists spokesman said the league was delighted by the announcement and sent their "warm greetings and congratulations" to the royal couple.
Prince Charles, Queen Elizabeth II's oldest son, is now No. 1 in the succession line.
No details were immediately available about when the third baby is due, but betting agencies were quick to start offering odds on possible names for the soon-to-be-born child in the House of Windsor.
The Palace added that a planned event for the Duchess today was canceled. "Whether they will be able to do that or whether the duchess will be well enough to do that also remains to be seen".
William and Harry have been in the headlines in recent weeks as they led the efforts to remember their mother Princess Diana who died in a auto crash in Paris 20 years ago last Thursday.
The child will be Queen Elizabeth's sixth great-grandchild. The baby will also be fifth in line to the heir to the throne.
She had the condition when she was pregnant with George and Charlotte as well.