“What a day of great joy for new parents,” said Rudd in a televised statement to the press.

“On behalf of all Australians, I send heartfelt congratulations to the Duke and Duchess of Cambridge on this joyful occasion.

“The birth of a baby is an experience to celebrate and cherish. We wish the new parents every happiness and send warm greetings of welcome to the little prince.”

“I think all Australians at the bottom of their hearts wish the Royal bub all the best, and certainly wish the new parents all the best as well.

“When a new bub comes into the world, any old day, any part of the world, it is frankly a time for rejoicing.”

“Prince William holds a special place in the hearts of many Australians. Some of us remember his first visit to this country as a 9-month-old baby more than 30 years ago with his mother Diana and father Charles…This is a happy day for our close friends in Britain and the Commonwealth.”

In New Zealand, prime minister John Key said ”I think New Zealanders will be celebrating with the happy couple and it’s great to see the birth of a future king of New Zealand so we wish them all the very best. It will be an exciting time for them.”

“The birth of a child is a time of great joy and excitement, and I know they will make excellent parents.”

The official announcement outside Buckingham Palace in London (Getty images)

British PM David Cameron said it was “a historic moment in the life of our nation…above all, it’s a wonderful moment for a warm and loving couple who have got a brand new baby boy.”

In the US, President Obama said in a statement: “Michelle and I are so pleased to congratulate The Duke and Duchess of Cambridge on the joyous occasion of the birth of their first child.

“We wish them all the happiness and blessings parenthood brings. The child enters the world at a time of promise and opportunity for our two nations. 

“Given the special relationship between us, the American people are pleased to join with the people of the United Kingdom as they celebrate the birth of the young prince.”

Amongst the royal baby excitement, the BBC mistakenly labelled Kevin Rudd the Prime Minister of Canada.