Amid all the cheers, the congratulations, the photographs with the Queen, nothing has been more memorable than the look on Harry’s face of sheer, unbounded joy.
Anyone who has seen the Prince with children knows what a terrific father he will be, and how much this moment means to him – not least because the birth of Archie is a major step on what has been a long and arduous journey towards one thing he has always craved: a ‘normal’ existence.
It has been a year since I published my biography of the Prince, based on more than 12 months of following him on official engagements.
He told me then how pressured he’d felt by his Royal status and the attention showered upon him.
He said he had even considered quitting the Royal Family altogether, so disillusioned was he by ‘the goldfish bowl’ of palace life.
‘I’m determined to have a relatively normal life,’ he said, ‘and if I am lucky enough to have children, they can have one, too.’
Now, it seems, that wish has been granted, in part at least.
Meghan, too, looked radiant, immersed in her new child. Yet the road ahead will not be easy because Harry finds himself alongside a wife who often seems to have little taste for the quiet life.
However homely the immediate moment, Meghan is beautiful, intelligent and ambitious, and intent on proving these qualities to the world, even at the risk of angering the Palace establishment.
As we shall see, there may be storm clouds ahead.
I can reveal that Buckingham Palace, unsettled by Meghan’s determination to do things her own way, has already taken decisive action to control her activities.
And in a clash between Meghan and the Royal authorities, there will only be one winner. As one source puts it: ‘The Palace always wins.’
It is clear that young people bring out the best in Harry – and that he knows how to bring out the best in them.
Even his appearance changes in the company of children. His eyes light up. He seems happy and at peace with himself.
I’ve seen this myself, such as when I joined him on an official visit to a sports group in Nottingham.
‘Wow’, he said, as he approached an eight-year-old boy. ‘Are you wearing new trainers? They’re great!’ I watched as, entranced, the child beamed and tried to follow Harry round the room.
Later I went ahead of the Prince to a youth group for children excluded from school. They had seemed bored and disaffected yet, when Harry arrived, it was like turning on a light.
He went round the room hitting the boys on the back and making the girls laugh. Within minutes they’d all gathered round him, begging for selfies. The hard man of Afghanistan has a very soft centre.
Fatherhood was something we talked about when we chatted at Kensington Palace. ‘Children don’t judge me,’ he said. ‘They just see me as someone who likes to have fun.’
Having his own son to love and protect could even help repair the damage of his own childhood, scarred by the toxic breakdown of his parents’ relationship and the loss of his mother when he was just 12. It comforts him to feel the presence of Diana.
‘There is still a lot of grief to be let out,’ he admitted to me shortly before he got engaged, adding: ‘I instinctively know what my mother would like me to do.’
Unlike his older brother, who is a direct heir to the throne, Harry has lacked a clear role in life.
Being a proud father should make him feel more valued. Meghan, too, has had a difficult background – as illustrated by the very public family rows and breakdown of the relationship with her father, Thomas.
Proudly self-reliant, she has been fortunate with good looks, drive and brains. Climbing the slippery slope of fame, however, has required her to be tough, ruthless even, and one consequence is the perception that she is willing to leave behind those she feels are no longer useful.
If fatherhood will be the making of Harry, the bigger question is: how will motherhood fit with Meghan’s seemingly limitless desire to prove herself?
Those who know her say Meghan’s true wish is to be seen as an international humanitarian, and everything from her public speeches on modish causes to her choice of A-list friends suggests they are right.
However much Harry longs to live away from the goldfish bowl, his choice of partner has made that much more difficult.
Harry told me in plain terms that he, William and Kate ‘are not a bunch of celebrities and do not want to go down a celebrity route’.
Meghan, it seems, has a different take – as became clear when she threw a star-studded £350,000 baby shower in New York, an event which, tellingly, Buckingham Palace knew nothing about.
The truth is that certain members of the Royal Household will feel relieved if the new mother takes her foot off the accelerator for a while.
The Duchess has rightly gained many fans who see her as a breath of fresh air and are delighted that she appears to be hauling the Royal Family into the 21st Century.
Yet Meghan has aroused the suspicion of some Palace insiders because of her apparent disregard for such long-established Royal values as caution and discretion.
The 12 months since she got married have been far from straightforward. She has been unable to prevent long-standing family disagreements becoming headline news and has lost a number of staff, including her press adviser.
She has often appeared to run her own publicity machine, in fact, disregarding courtiers in the process.
Indeed, insiders are laying last week’s PR fiasco around Archie’s birth at her door.
While it was announced that the Duchess had gone into labour at 1.49pm on Monday, she had actually given birth eight hours earlier.
Others in the Royal set-up have been concerned to find that, several times, public appearances by Meghan and Harry have clashed with scheduled engagements for more senior Royals, including Prince Charles.
Buckingham Palace, I can reveal, has concluded that this can’t go on and has already put its foot down.
The recent announcement that the Sussexes are to move their offices from Kensington Palace to Buckingham Palace was interpreted as a sign that Harry and Meghan wished to go their separate way from William and Kate, who remain at the offices they used to share.
But a senior source told me this move was meant as a tactful yet firm way of working more closely with both the Duchess and her husband, who seems, for the moment at least, determined to follow her lead.
‘The decision was made before his wedding when Kensington Palace began issuing daily statements about Meghan Markle’s father,’ I was told.
‘Buckingham Palace was horrified. A key part of being Royal is that you don’t say anything about that sort of thing. The Palace abides by its mantra, ‘When in doubt, never speak out.’ ‘
Meghan, however, has been keen to drive public discussion as she thinks best. Take that Manhattan baby shower. Had Buckingham Palace known in advance, I was told, they would have prevented it.
Just as significant as the move of offices is the fact that Sara Latham, the couple’s new communications director, will come under the direct control of the Queen’s communications secretary, Donal McCabe.
And the Queen’s staff will keep a close eye on the Sussexes’ diary. ‘They decide what to put in front of the senior Royals,’ said my source. ‘It’s a bit like the civil service. Engagements are scheduled by committee. Diaries are cross-referenced to ensure there isn’t a clash and they decide if an event is suitable.’
Another Royal insider confirmed: ‘The intention is to ensure what they do is co-ordinated with the rest of the household so you don’t get an Independent State of Frogmore [the Sussex’s Windsor cottage].
‘The Royal Family is a very hierarchical organisation. It’s the Queen, Prince Charles, the Cambridges, the Sussexes in that order. As the fourth household you have to respect that chain of command.’
Insiders also say the new structure gives Ms Latham an excuse in case she needs to say ‘no’ to Harry and Meghan.
‘If there’s a difficult conversation to be had, she can say it’s Donal McCabe blocking this, not me,’ said the source. ‘This isn’t control in the sense of limitation. The Sussexes are well-liked. The message is simply: don’t let the good you do obscure that of others.’
Not that Meghan is a soft touch. She has already shown she has few qualms about working outside the Royal machine.
No one doubts she authorised her friends to speak to an American celebrity magazine about the ‘global bullying’ of her.
But getting it right is another matter altogether. The farce surrounding the announcement of Archie’s birth has caused dismay within an organisation used to operating with the most certain touch.
One Palace insider told me he was in no doubt that Meghan and Harry had pulled the strings.
‘The way the birth was handled was a huge cock-up and left a very confusing picture,’ he said.
‘The Sussexes were determined to get what they wanted. But the Palace machine is a force to be reckoned with.’
A former member of the Royal Household took up the theme: ‘Everyone who comes into the Royal Family needs a bullet-proof raincoat. Princess Diana called those in control ‘the grey winds’ and saw them as a ‘malign dark force’.
‘She used to contact the newspapers herself as a last resort as there was no one she felt she could trust at the Palace. The Duchess is echoing her behaviour.’
There was a pause before he added, menacingly: ‘The life of the Duchess of Sussex could be made very difficult and awkward if she doesn’t conform. Harry will have recognised this.’
One must hope that the Prince has the wisdom to help his wife negotiate Royal protocol without stifling the charismatic American free-spiritedness he fell in love with.
As for Archie, Harry will want to protect his son’s privacy and keep the young boy out of the public eye.
He has long harboured an understandable but entirely unjustified sense of guilt that he was unable to protect his mother.
Now that protective side will be lavished on Archie and hopefully – for a time at least – he and Meghan can set aside Palace politics and revel in their ‘little bundle of joy’.
The paperback edition of Harry: Conversations With The Prince by Angela Levin will be published by John Blake on May 30, priced £8.99.