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

The Duchess of Cambridge and her husband left the Lindo Wing at St Mary's Hospital in London shortly before 5am (NZT), just seven hours after giving birth to her third child, weighing 8lb, 7oz.

A few hours earlier, during a photo call with his new son on the steps of the hospital, 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).

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

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.

They then re-emerged with the baby in a carseat just before 5am NZT.

William joked that he didn't keep world waiting for too long after she went into labour at around 5pm Monday, NZT before giving birth five hours later.

He said of the name of the new baby: "You'll find out soon!" He also joked that he and Kate would have "Thrice worry now!"

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

The baby is fifth in line to the throne and the Queen and the Duke of Edinburgh's sixth great-grandchild.

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

Earlier, the new baby's older siblings, Prince George and Princess Charlotte, were taken to meet him in their school uniform nearly six hours after Kate gave birth.

By the time the new baby was being shown off to the world, George and Charlotte had already returned to Kensington Palace.

The Royal couple pose for the media after leaving the hospital. Photo / AP
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
Britain's Prince William and Catherine, Duchess of Cambridge with their newborn baby son. Photo / AP

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.

"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.

Britain's Prince William arrives with Prince George and Princess Charlotte back to the Lindo wing at St Mary's Hospital in London. Photo / AP
Britain's Prince William arrives with Prince George and Princess Charlotte back to the Lindo wing at St Mary's Hospital in London. Photo / AP

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.

Prince George, still wearing his school uniform, was the first to get out the Land Rover Discovery, which was driven by his father.

He was followed shortly afterwards by his sister Princess Charlotte, who waved to the cameras with one hand and held the Duke of Cambridge's hand with the other.

Hand-in-hand, all three walked up the steps into the hospital to meet the new arrival - but not before Princess Charlotte turned around once more to wave at the massive crowd outside.

The new Prince was born at 11.01am (10.01pm NZT) with Prince William alongside the Duchess, who had been taken to hospital having gone into labour at at 6am. Kensington Palace announced the new prince weighed 8lb 7oz.

Princess Charlotte waves at the crowds outside the hospital when she arrived to meet her baby brother. Photo / AP
Princess Charlotte waves at the crowds outside the hospital when she arrived to meet her baby brother. Photo / AP

Champagne corks popped and cheers rang out outside the Lindo Wing as the birth of a new Prince of Cambridge was announced at just after 1pm. The baby's sex was a surprise to William and Kate, who chose not to find out in advance.

Mother and baby are "doing well", while the Queen, Prince Philip and other senior members of the Royal family are said to be "delighted" with the news.

It is expected the prince's first name will be announced in the coming days, with predictions including Arthur, Albert, Frederick, James and Philip.