His younger sister, Lilibet “Lili” Mountbatten-Windsor, is also entitled to be a princess following the death of the Queen and with her grandfather, the Prince of Wales, becoming King.
The rules set out by King George V in 1917 mean Archie and Lili – as the children of a son of a sovereign – also now have an HRH style if they choose to use it.
In 2021, it was suggested Charles – in a bid to limit the number of key royals – intended, when he became monarch, to prevent Archie becoming a prince.
To do so, he will have to issue a Letters Patent amending Archie’s right to be a prince and Lili’s right to be a princess.
Until that potentially happens or if it does not, Archie and Lili remain a prince and princess, whether their parents choose to use the titles or not.
Meghan argued in the Sussexes’ bombshell interview with US talk show host Oprah Winfrey that Archie was not given the title of prince because of his race.
However, when Archie was born seventh in line to the throne in May 2019, he was too far down the line of succession.
Although he was a great-grandchild of the monarch, he was not a first-born son of a future king, so was not automatically a prince.
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He could have previously used the courtesy title Earl of Dumbarton, or been Lord Archie Mountbatten-Windsor.
But Buckingham Palace said the duke and duchess made a personal decision that he should be plain Master Archie Mountbatten-Windsor instead.
A royal source said following Archie’s arrival that the couple had chosen not to give him a courtesy title “at this time”.
Meghan also told Oprah that, when she was pregnant with Archie, an unnamed member of the royal family had raised “concerns and conversations about how dark his skin might be when he’s born”.
The Sussexes stopped using their own HRH styles after stepping down as senior working royals for a life in Los Angeles, and there were later calls for their duke and duchess titles to be removed.
If Harry and Meghan decide that Archie and Lili will be known as a prince and a princess, this will stand in direct contrast to how Harry has always spoken about the burden of having a title.
He repeatedly stressed the importance of wanting to be seen as normal and confessed in 2017 that he once “wanted out” of the royal family – a wish that became a reality in 2020.
The former soldier said the time he spent in the Army, when he was “just Harry”, was “the best escape I’ve ever had” and he had considered giving up his title.
Royal author Penny Junor said: “He would have dearly liked to have been a normal boy growing up, and found his title very difficult.”
The duke is close to his cousins, Zara Tindall and Peter Phillips, and may have taken their experiences on board.
Junor added: “He looked at Zara and Peter and it was so much easier for them than for him.
“He was constantly the centre of attention. His friends were targeted whenever he did anything wrong or misbehaved in any way.
“We knew nothing about Zara or Peter when they were growing up because they were ordinary children going to ordinary schools and were not being treated in any special way.”
Zara, who grew up as Miss Zara Phillips, was not entitled to be an HRH because she was born in the female line as the offspring of the daughter of a sovereign.
She has spoken of how not having a title was a blessing.
“I’ve been very lucky. My parents didn’t give us titles, so we’ve been able to have a slightly more normal upbringing. As soon as you’ve got a title, it’s very difficult to shed it,” she said.
The Earl and Countess of Wessex’s daughter, Lady Louise Windsor, and son, Viscount Severn, as the children of the son of a monarch, were allowed to be known as princess and prince.
But Edward and Sophie, with the Queen’s permission, decided to use the courtesy titles of an earl instead.
Meghan said she and Harry wanted Archie to be a prince so he would have security and be protected.
But being a prince or princess does not automatically mean royals have police bodyguards paid for by the taxpayer, and the Sussexes have chosen to live in the US.
Archie is technically history’s first Prince of Sussex and Lili the first Princess of Sussex.
The previous 19th century Duke of Sussex – an eccentric son of King George III – had both his marriages deemed illegal.
His mistress, Lady Augusta Murray, was not the Duchess of Sussex and his illegitimate son was plain Master Augustus Frederick d’Este.
Lady Augusta did, however, continually refer to herself as a duchess and a princess, and staff called her son Prince Augustus and her daughter Princess Augusta.
Eventually Archie will be entitled to succeed Harry as the Duke of Sussex.