Princess gets warm g'day from Aust

Britain's newest royal has received a warm g'day from Australia.

The Prime Minister has led a chorus of congratulations to the Duke and Duchess of Cambridge.

"The birth of a baby is a great moment for any family and Australia shares this young family's joy," Mr Abbott said in a statement on Saturday night.

"We wish the young Princess a long and happy life.

"I am sure that the Princess and her older brother, Prince George, will in time develop a deep familiarity and love of Australia, feelings the rest of their family already share."

Mr Abbott said the Australian people would send their best wishes to the new parents at a special time in their lives.

Kensington Palace announced the birth just after 8pm Australian time though the name of the baby princess was not immediately made public.

Australia's Governor-General and Lady Cosgrove said they were "thrilled" by the news.

"We hope Their Royal Highnesses enjoy this special time as well as the life of fond memories they will build together as a family," the Governor-General, Sir Peter Cosgrove, said in a statement.

"We look forward to seeing the whole Cambridge family in Australia sometime in the future."

Australians for Constitutional Monarchy executive director Jai Martinkovits said the arrival of baby royals had the effect of personalising the monarchy.

"The birth of a new member of the royal family is also something which unites people," Mr Martinkovits told AAP.

"There is a lot of turmoil globally - politically and otherwise - and having something that brings people together in a warm way is a positive."

The princess's uncle, Prince Harry, who is in Australia on military service, was at a Perth stadium watching an AFL game when the birth was announced.

A photo of the prince watching West Coast Eagles beat the GWS Giants circulated on Twitter.

"Your sister-in-law has a baby and you go to the footy ... #wellplayed," tweeted Seven Network reporter Matt Tinney.