The sweet detail we missed during Prince Harry's baby announcement

The Duke of Sussex was a picture of pride when he announced to the world the arrival of his son on Monday.

Just hours after the Duchess, 37, finally gave birth to their first child, the new dad held a casual press conference, where reporters congratulated him and took turns shaking his hands.

Prince Harry, 34, talked about how "amazing" it was to watch his child being born, and how proud he was of wife Meghan, 37.

Following his announcement, the Duke revealed off camera that he'd had very little sleep.

"I've had about two hours' sleep,” Hello! reports the prince as saying.

We know Baby Sussex arrived late, with Prince Harry confirming the baby was “a little” overdue.

It is thought Meghan went into labour at home before being transferred to a hospital to give birth.

During the official portion of the press conference, Prince Harry gushed about the experience.

"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. It's been amazing, so we just wanted to share this with everybody,” he added.

We reveal all the details of Baby Sussex on a special bonus episode of The Windsors. (Article continues.)

"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."

Baby Sussex will make his first public appearance on Wednesday.

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Meghan, the Duchess of Sussex's life in photos