Royal baby: Duke and Duchess of Sussex introduce Archie Harrison

The Duke and Duchess of Sussex have revealed their son has been named Archie Harrison Mountbatten-Windsor.

The couple made the announcement via their Instagram page, along with a picture of Meghan holding Archie, and showing him to the Queen, Prince Philip,her mother Doria Ragland, with Prince Harry watching on.

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"The Duke and Duchess of Sussex are pleased to announce they have named their first born child: Archie Harrison Mountbatten-Windsor," the post read.

"This afternoon Their Royal Highnesses introduced Her Majesty The Queen to her eighth great-grandchild at Windsor Castle. The Duke of Edinburgh and The Duchess' mother were also present for this special occasion."

The name Archie comes from the British name Archibald and Harrison is an Indigenous name, which means "son of Harry".

He will be known as Master Archie Mountbatten-Windsor.

It came just hours after the new family attended their first photocall as a family of three in the majestic St George's Hall in Windsor Castle, which was an intimate affair of a small media crew.

Covered in a white blanket and bonnet, the baby appeared to be sleeping soundly in his father's arms, as his parents beamed down at him.

"It’s magic, it’s pretty amazing," the Duchess said.

"I have the best two guys in the world."

When asked about his temperament, Meghan said: "He has the sweetest temperament, he's really calm," as Harry joked "I wonder where he get’s that from," and the pair laughed.

Meghan added: "He's just been the dream so it's been a special couple of days."

Asked who the baby takes after, Meghan said: "We're still trying to figure that out."

Harry said: "Everyone says that babies change so much over two weeks. We're basically monitoring how the changing process happens over this next month really. But his looks are changing every single day, so who knows."

When they were asked to show more of their son's face to the cameras, Meghan laughed as Harry joked: "He's already got a little bit of facial hair as well, wonderful."

"Thank you everybody for all the well wishes and kindness, it just means so much," Meghan said.

Before the Duke and Duchess introduced Archie to the Queen and Prince Philip, Meghan revealed they had "bumped into" the Duke in the castle before the photocall.

"We just bumped into the duke as we were walking by, which was so nice," she said.

"So it'll be a nice moment to introduce the baby to more family, and my mum's with us as well."

Harry added: "Another great-grandchild."

Meghan and Harry shared a few pictures on their Instagram page after the photocall, thanking the public for their support.

The couple has been enjoying the experience of being new parents at their Frogmore Cottage home near the Queen's Windsor Castle residence.

The Duchess of Sussex gave birth at 5.26am on Monday, and is thought to have been born the couple’s house, however there are some reports claiming the baby was delivered in a London hospital.

Harry was at his wife's side during the birth and he later confessed he had only had a few hours' sleep, suggesting Meghan had spent much of the night in labour.

The beaming Duke of Sussex spoke to news cameras in Windsor less than an hour after Buckingham Palace revealed Meghan had gone into labour, describing his son as "absolutely to die for".

"How any woman does what they do is beyond comprehension but we're both absolutely thrilled and so grateful to all the lovely support from everybody out there," the new father said.

"It was amazing, absolutely incredible. As I say, I am so incredibly proud of my wife and, as every father and parent would ever say your baby is absolutely amazing, this little baby is absolutely to die for."

Family members have spoken about the joy of the new arrival, with the Duke of Cambridge saying he was: "obviously thrilled, absolutely thrilled, and obviously looking forward to seeing them in the next few days when things have quietened down".

"I'm very pleased and glad to welcome my own brother into the sleep deprivation society that is parenting," he added.

Kate said they were eager to see the Sussexes and their new arrival.

"As William said, we're looking forward to meeting him...so it's really exciting for both of them and we wish them all the best," she said.

"These next few weeks are always a bit daunting the first time round so we wish them all the best."

The Prince of Wales has also spoken publicly for the first time about the birth, saying he was "delighted" at arrival of his latest grandchild.

During an official visit to Germany with the Duchess of Cornwall, Charles said: "We couldn't be more delighted at the news and we're looking forward to meeting the baby when we return."

The Queen accepted the congratulations of a Windsor Castle guest who asked: "Life is good for Your Majesty?"

The Queen, who was joined by the Duke of Edinburgh, was hosting a lunch on Tuesday for members of the Order of Merit and smiling said in reply "yes, thank you".

The infant is believed to be the first mixed-race child born to a senior member of the royal family in centuries, and is a reflection of modern Britain with its culturally diverse population.