Meghan Markle was able to fulfil her wish to have a home birth, it is believed.
The Duchess of Sussex is thought to have given birth at Frogmore Cottage at 5.26am today.
It has been reported the 37-year-old was keen to have a home birth as part of an effort to enjoy more privacy than the Duke and Duchess of Cambridge.
An official statement from Buckingham Palace this afternoon appeared to indicate the birth was at the Duke and Duchess's home in the grounds of Frogmore House.
It had been feared that because the former Suits star was overdue she may have to go to hospital to be induced.
Daily Mirror Royal Editor Russell Myers said it is believed the Duchess of Sussex did manage to fulfil her wish of having a home birth.
He said: "Although there has been no formal announcement from Buckingham Palace, it is understood that Meghan did give birth at home at the couple's Frogmore Cottage.
"Having a home birth had been very important to Meghan but as she was overdue there had been fears that she may have to be induced, which would have almost certainly meant she would have had to go into hospital.
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"Having a home birth means that Meghan has very much gone back to the practice that was employed by almost all royal women historically.
"Thankfully, it seems as though nature has taken its course and Meghan successfully delivered a healthy baby boy a little more than a week over her due date.
"In 1970 Princess Michael of Kent gave birth to her first child at St Mary's hospital in Paddington, London and posed outside the hospital afterwards.
"This set forth a tradition of many royal women doing the same over the last 49 years, including the Duchess of Cambridge who had all three children at the Lindo Wing of St Mary's.
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"Both Meghan and baby are understood to be doing very well and we can expect to see them with Prince Harry as a family for a small photocall so they can introduce their little one to the world on Wednesday."
Baby Sussex is yet to be named but his dad Prince Harry looked thrilled when he briefly spoke to reporters at Windsor Castle this afternoon.
The Duke and Duchess of Sussex are keeping details of the birth private for now, but the place of birth is likely to be revealed on the birth certificate.
Royal babies were traditionally born at home, usually in royal palaces.
The Queen kept to the custom for all of her own four children, the Prince of Wales, the Duke of York and the Earl of Wessex were born at Buckingham Palace, while the Princess Royal arrived at Clarence House.
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When delivering Charles, Princess Elizabeth was given an anaesthetic to help ease the pain.
A restless Duke of Edinburgh played squash with his private secretary while his wife was in labour.
He was still on the courts at the palace when he learned of his son's arrival, after King George VI's private secretary rushed out to announce the birth.
Buckingham Palace said in a statement: "Her Royal Highness the Duchess of Sussex was safely delivered of a son at 0526hrs.
"The baby weighs 7lb 3oz. The Duke of Sussex was present for the birth.
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"The Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall, the Duke and Duchess of Cambridge, Lady Jane Fellowes, Lady Sarah McCorquodale and Earl Spencer have been informed and are delighted with the news.
"The Duchess's mother, Doria Ragland, who is overjoyed by the arrival of her first grandchild, is with their Royal Highnesses at Frogmore Cottage.
"Her Royal Highness and her child are both doing well."
