"Mother and baby are doing incredibly well".
"It's been the most incredible experience I could ever have possibly imagined", he said.
What began as a blind date for the two back in 2016 has evolved into a marriage, new royal titles and the start of a family for the husband and wife.
When did Meghan announce her pregnancy?
"Their Royal Highnesses have appreciated all of the support they have received from people around the world since their wedding in May and are delighted to be able to share this happy news with the public".
Addressing his 6.64m followers, Piers said: "Trying, but now failing, to muster up a semblance of enthusiasm for this royal baby story before tomorrow's GMB".
A royal commentator has suggested that palace aides may have been caught off guard by the arrival of the Duke and Duchess of Sussex's baby.
LISTEN: This new bonus episode of The Windsors podcast answers all your burning questions about baby Sussex.
Names including Arthur, James and Albert are now hotly tipped by British bookmakers to be chosen by the couple.
Harry said the child was a little bit overdue and that had given them more time to contemplate names.
Where did Meghan give birth?
That said, there is one reason Baby Sussex may want to opt out of his American citizenship when he's older.
There was fevered speculation in recent weeks over everything from the newborn's gender and name - to whether it will have Harry's ginger hair.
Asked what it was like to be present for the birth, he laughed and said: 'I haven't been at many births.
What happened after the birth?
The as-yet-unnamed infant was believed to have been born in the sanctuary of Frogmore Cottage - the Sussexes' home on the Windsor Estate.
It's official: Meghan Markle is a mom.
After the announcement was placed outside, hoards of well-wishers gathered by the palace's gates to see it for themselves.
Royals tend to take their time about naming a baby.
On International Women's Day, for example, Markle said this: "I think the real treat in and of itself is being able to be here-that is such a gift on this day".
What will the baby be called?
Extended stays The Portland can rack up bills of £1,800 a night, a far cry from Frimley Park NHS Hospital in Surrey where Meghan and Harry were rumoured to have gone if her hopes of a home birth were dashed.
It is also possible Harry and Meghan will break tradition and give the baby a name without a long connection to the royal family.