UPDATED 10.09am: The Prime Minister has congratulated the royals on their second child.

John Key says the Duke and Duchess are excellent parents and he's sure Prince George will adore his new little sister.

New Zealand will be sending an official gift of woollen baby items including a pelt teddy bear.

It comes as the world caught its first glimpse of Prince William and Kate's new baby girl, with the trio posing for photographers before leaving St Mary's hospital in London.

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The royal couple and their new bub left the private Lindo Wing on Saturday evening (Sunday morning AEST) less than 10 hours after Kate gave birth at 8.34am local time.

The new princess - who is fourth in line to the British throne - was wrapped in a white shawl and was wearing a cream baby hat for her first public appearance.

Kate carried her daughter out of the Lindo Wing's front door before posing for a few minutes with William.

The duchess was wearing a yellow and white summer dress and high heels.

Prince William was dressed in a white shirt, a blue v-neck jumper and dark blue slacks.

After waving to supporters the royal couple returned inside before re-emerging minutes later with William carrying the newborn princess in a baby carrier.

He put his daughter in the back of a black Land Rover before the Cambridges drove off to Kensington Palace.

Kate gave birth to a daughter weighing 3.7kg less than three hours after she was admitted to hospital at 6am.

In the afternoon the duke left St Mary's briefly to pick up Prince George at Kensington Palace before returning to introduce the 21-month-old future king to his baby sister.

"I'm very happy," a smiling William said.

He carried Prince George on one arm and waved to supporters.

The little prince waved too. He was dressed in matching white and blue.

Prince George left the Lindo Wing quietly through a back entrance sometime before William, Kate and his new baby sister departed around 6.15pm local time.

Saturday's posing on the hospital steps was reminiscent of July 2013 when the Cambridges showed off Prince George for the first time.

There were also echoes of 1982 when, at exactly the same spot, Princess Diana stood holding the infant duke alongside husband Prince Charles.