Kate and William show the world their baby princess

The Duke and Duchess of Cambridge have arrived home with their new baby daughter just hours after she was born this morning.

The couple emerged on the steps outside the Lindo Wing at St Mary's Hospital and the world was given a brief glimpse of the new princess, who was wrapped in a white blanket.

A close-up of the new princess. Photo / Screengrab / Sky News

The newest royal, who is name is not yet known, was born at 8.34am on Saturday UK times weighing 8lbs and 3oz - less than three hours after the Duchess was admitted to hospital.

She was soundly asleep when her parents presented her to the cameras and the crowds of well-wishers camped outside the hospital.

Prince William and Kate smiled and waved as they posed for pictures with their new baby then briefly returned to the hospital.

They then emerged again, with Prince William carrying his sleeping baby in a car seat. He loaded her into the back of a people carrier before they all drove off to Kensington Palace.

In a statement posted on the royal Twitter account, the couple said: "Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have all received.

"They would also like to thank everyone for their warm wishes."

Earlier in the day, Prince William took Prince George to the Lindo Wing to meet his newborn sister. The 21-month-old almost stole the show when he gave a timid wave to the crowds from the hospital steps.

Cheers erupted for the young prince, who has not made a public appearance in the UK since his own birth in 2013, as he made his way towards the Lindo Wing in his father's arms.

He was driven from the family home at Kensington Palace to St Mary's Hospital by his father, Prince William, and stayed for about an hour before he was taken back home for his bath and tea with his nanny.

Prince George, in his father's arms, steals the show on a visit to his little sister.Prince William told the crowds he was very happy as he headed off to pick up Prince George. Photo / Getty Images

When they arrived, William carefully took George out from his safety seat in the back of the Range Rover and could be seen whispering a few reassuring words.

He attempted to put the toddler down but George, dressed in a blue jumper, shorts and socks, was having nothing of it and William picked him up again.

There was, however, a half smile for the cameras and a little wave over his father's shoulder as they walked inside. William also tenderly kissed his first born son on the head.

William had beamed with pride as he left hospital to pick up George. Before getting into his black Range Rover, he said: "we're very, very happy."

- NZME