“It’s been the most amazing experience I can ever possibly imagine,” the Duke of Sussex said, smiling and laughing.
“How any woman does what they do is beyond comprehension,” he said incredulously, waving both hands in the air.
“We’re both absolutely thrilled and so grateful for all the love and support from everybody out there, it’s been amazing, so we just wanted to share this with everybody.”
Harry added that the two had extra time to brainstorm baby names, as Meghan Markle was overdue.
Harry added: “I haven’t been at many births. This is definitely my first birth – it was amazing, absolutely incredible.
“I’m so incredibly proud of my wife. And as every father and parent would say, your baby is absolutely amazing.
“But this little thing is absolutely to-die-for so I’m absolutely over the moon.”
The seventh in line to the throne baby boy – an eighth great-grandchild for the Queen and the Duke of Edinburgh – arrived at 5.26am, weighing 7lb 3oz.
A hastily arranged live press conference to announce the good news saw a small group of media ushered into the grounds of Windsor Castle, and as they passed the duke, chatting with an aide, he immediately looked up smiling and waved hello.
The as-yet-unnamed baby boy is believed to have been born in the sanctuary of Frogmore Cottage – the Sussexes’ home on the Windsor Estate.
Harry was at his wife’s side during the birth and was clearly moved by the experience.
The Queen and Philip, grandfather the Prince of Wales, and the Duchess of Cornwall and the Duke and Duchess of Cambridge are all said to be delighted with the news.
The palace statement also mentioned the siblings of Harry’s late mother Diana, Princess of Wales, who died in a car crash when he was 12.
“Lady Jane Fellowes, Lady Sarah McCorquodale and Earl Spencer have been informed and are delighted with the news,” the statement said.
Meghan’s mother is with the new family of three at Frogmore Cottage.
“The Duchess’s mother, Doria Ragland, who is overjoyed by the arrival of her first grandchild, is with their Royal Highnesses at Frogmore Cottage,” the palace said.