Prime Minister Scott Morrison has warmly recalled his meeting with the Duke and Duchess of Sussex last year and congratulated them on the birth of their son.
Prince Harry and wife Meghan announced they were expecting a baby on the first day of their visit to Australia in October.
The baby, who is seventh in line to the throne, was born on Monday weighing 3.26 kg.
"A baby coming into anyone's life whether you are a royal or not, whether you are living in Albury-Wodonga or in the southern suburbs of Sydney or in Cloncurry, it doesn't get any better than that," Mr Morrison told reporters in Albury, NSW on Tuesday.
"The fact that everybody is healthy and everybody is well, it is a nice reminder that there are some really good things in this world."
He said it was a great thrill when he and his daughters met the royal couple when they came to Australia on their first international tour after getting married.
"Jenny cooked the pav and Prince Harry smashed the pav. He absolutely loved it," the prime minister said.
"Maybe we will have to get one over there for the new baby."
Labor Leader Bill Shorten also congratulated the couple.
"Chloe and I are delighted for Harry and Meghan on the arrival of their baby boy. They are a lovely couple and will make wonderful parents," he tweeted.
As congratulatory messages flood in from all over the world, questions have turned to the baby's name and his title.
Unless the Queen intervenes, the baby won't be called 'His Royal Highness' or carry the title of prince due to rules limiting titles within the royal family.
"I think the Queen would be in favour of it," Australians for Constitutional Monarchy head David Flint says.
"It may well be that they (Harry and Meghan) decide not."
Professor Flint said it's likely the Duke and Duchess of Sussex will choose a traditional name for their son, although a modern name was possible.
Punters are betting on Philip and James as the most likely, followed by Edward.
The Australian Republic Movement has also "warmly" congratulated the royal couple, along with "all Australians who welcomed a child into the world today".
