The baby has been described by his proud father as "absolutely to die for."

The baby, who has not yet been named, was born in the early hours of the morning weighing 7 lbs 3oz (3.26 kg). Meghan, a U.S.-born former actress, and the baby, the couple's first child, were both healthy and well, the palace said.

"How any woman does what they do is beyond comprehension but we're both absolutely thrilled and so grateful to all the love and support from everybody out there," a smiling Harry told reporters in Windsor, west of London where the couple live.

"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 thing is absolutely to die for."

Harry, Queen Elizabeth's grandson, was present for the birth and Doria Ragland, Meghan's mother, was with the couple at their home, Frogmore Cottage, on the estate of Windsor Castle where they married in a lavish ceremony in May last year.

The baby is the eighth great grandchild of the 93-year-old queen, the world's longest-reigning monarch, and could be entitled to hold joint British and American citizenship according to nationality rules.

However, the child will not automatically be a prince or a princess and any such title would have to be bestowed by the queen by issuing what is known as a letter patent.

The queen and other members of the royal family, including the sister and brother of Harry's late mother, Princess Diana, were delighted by the news of the birth, the palace said.

Britain's royal family attracts huge media interest but the younger members, especially Harry, 34, and Meghan, 37, are treated like Hollywood superstars.

Their baby is the first mixed race baby born into a senior position in British royalty, according to royal experts.

For some this is a significant moment for the monarchy. Others note however that Meghan, whose mother is African-American and father is white, has been the target of racist commentary on social media.

"It's symbolic of a more modern monarchy. It appeals to people across the world," royal biographer Claudia Joseph told Reuters. "They will be able to identify with the royal family as never before."

Harry and Meghan used their official Instagram account to announce the birth, in modern fashion. But in accordance with a tradition dating back at least to 1837 when Buckingham Palace became the sovereign’s official residence, some hours later a notice announcing the birth was posted on a ceremonial easel on the forecourt of Buckingham Palace.

The palace did not confirm whether Meghan gave birth at home. While the late Princess Diana gave birth to Harry and his older brother William in hospital, the queen's four children were all born at Buckingham Palace.

James, Alexander, Albert, Philip, and Arthur are among the favourite names for the child, according to bookmakers.

"We're still thinking about names," Harry said. "The baby's a little bit overdue so we've had a little bit of time to think about it ... that's the next bit."

Meghan's father Thomas Markle, a former lighting director for U.S. TV soaps and sitcoms, said he was delighted at the news.

"I am proud that my new grandson is born into the British royal family and I am sure that he will grow up to serve the crown and the people of Britain with grace, dignity, and honour," he said in a statement to the Sun newspaper.

'Tops the wedding'

Unlike Prince William and his wife Kate, who posed for massed photographers outside a London hospital just hours after their three children were born, Harry andMeghan are expected to take part in only a limited photo call in the grounds of Windsor Castle in the next couple of days.

Harry has held a special place in the hearts of many Britons since millions around the world watched him, aged just 12, walk slowly behind his mother's coffin as the funeral cortege made its way through the packed streets of London after Diana's death in a Paris car crash in 1997.

In his youth, he found himself in the headlines for under-age drinking, wearing a Nazi outfit to a costume party and scuffling with photographers outside London nightclubs.

But after a successful stint in the army, where he served two tours of duty in Afghanistan, his relaxed style and playful antics when on official engagements have seen him become one of the most popular members of the royal family.

"It means an awful lot to me. This tops the wedding," said royal fan John Loughrey, 64, from London, who said he had been sleeping out in Windsor for the last three days. "They've brought a royal baby into the world, we're all excited."

Harry's marriage to Meghan, a divorcee hailing from Los Angeles who starred in the U.S. TV legal drama "Suits", has only increased global interest, bringing in a new army of royal fans.

"For Anglo-American relationships it's going to be very important because suddenly there's a child in the House of Windsor that is half-American," said Ingrid Seward, editor of Majesty Magazine.

"This is their entry into the royal family."

While Harry has gained plaudits for talking about his struggle with mental health issues, Meghan, has been vocal on feminist causes.

"I'd seen this documentary on Netflix about feminism and one of the things they said during pregnancy was 'I feel the embryonic kicking of feminism'," she said during an engagement in March. "I love that. So boy or girl or whatever it is, we hope that that's the case, with our little bump."

Their baby will be brought up in the couple's newly-refurbished home in Windsor, where they only recently moved.

They have also set up their own office, breaking away from the joint operation they shared with Prince William and Kate.

Britain's media has been rife with speculation about a rift between the brothers and their wives, although there has been no public indication of any disagreements.

However, some British newspapers have reported that Harry and Meghan might move abroad, most likely to Africa, after the birth as they seek to forge their own royal role.