Kate and William have shown off their new baby boy to the world - "thrice the worry now', said William, as their new son gave his first royal wave.

The Duchess of Cambridge and her husband emerged from the Lindo Wing at St Mary's Hospital in London shortly before 5am (NZT), just seven hours after giving birth to her third child.

Prince William said Prince George and Princess Charlotte were "delighted" about the arrival of their little brother who was born at 11.01am (10.01pm, Monday, NZT).

William joked that he didn't keep world waiting for too long after she went into labour at around 6am (5pm, NZT) before giving birth at 11am (10pm, NZT).

He said of the name of the new baby, who is now fifth in line to the throne: "You'll find out soon!" He also joked that he and Kate would have "Thrice worry now!"

The beaming parents looked delighted as they showed off their third son to the world who was born weighing 8lbs 7oz on St George's Day.

Towards the end of the Royal baby's first outing, the Duchess of Cambridge murmured to Prince William that she was worried about the baby getting cold before they headed back inside.

His older siblings, Prince George and Princess Charlotte, were taken to meet him in their school uniform nearly six hours after Kate gave birth, but were not present as their parents emerged from the Lindo Wing.

The Duchess of Cambridge left St Mary's Hospital just before 5am NZT, adding that George and Charlotte had already returned to Kensington Palace after meeting their new brother.

Earlier, Kate Middleton posed on the steps outside the central London hospital where the world's media and well-wishers had gathered to celebrate the Royal family's new arrival.

The Royal couple posed for pictures with the Duchess wearing a red dress and holding her son who was nestled in a white blanket.

 Britain's Prince William and Catherine, Duchess of Cambridge wave as they hold their newborn baby son as they leave the Lindo wing at St Mary's Hospital in London. Photo / AP

New mum Catherine, Duchess of Cambridge gazes at the latest addition to Britain's royal family. Photo / AP

As he left, the duke told reporters he was "very happy, very delighted, thank you".

In a statement, Kensington Palace said: "Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have received.

The Royal couple pose for the media after leaving the hospital. Photo / AP

Britain's Prince William and Catherine, Duchess of Cambridge with their newborn baby son. Photo / AP

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

On Monday afternoon, at 4.21pm, Prince William walked down the steps outside the central London hospital where the world's media and well-wishers had gathered to celebrate the Royal family's new arrival.

Half an hour after the Duke of Cambridge left the Lindo Wing after his wife gave birth, the now father-of-three returned with his two eldest.