"Welcome to our village wee one," Ardern wrote on Instagram at 6.15pm on Thursday.
Former New Zealand Prime Minister Helen Clark has written an opinion piece of the Guardian in the UK, praising current prime minister Jacinda Ardern and her partner Clarke Gayford for showing that "no doors are closed for women".
Ardern and Gayford announced the arrival of their first child,a baby girl, this afternoon.
The yet-unnamed baby was born in Auckland Hospital at 4:45pm, today, 21 June.
Clark wrote in the opinion piece that the couple's new baby has "considerable significance" for the country as a whole.
"Ardern becomes only the second serving second prime minister in history to give birth. As well, she is not married to her partner," Clark wrote.
She points out that Ardern has pointed all naysayers wrong and, alongside stay-at-home dad Gayford, she is redefining the family stereotype and showing that maybe women can have it all.
"Conventional wisdom may have said that this combination of factors would not have been helpful to a political career at the highest level. Fortunately, that has proved to be wrong," Clark added.
The former PM said the new mum is a "remarkable woman who crashes through glass ceilings with apparent ease".
She also commended Gayford for taking on the role of primary carer for the foreseeable future, as Ardern returns to her job of prime minister after six weeks of maternity leave.
"For young women, the example Ardern is setting is an affirmation that they too can expect to have that choice. For young men, Gayford being the full time carer of a baby sends a powerful message that they too can exercise that choice."
According to Clark, New Zealand is "breaking new ground" with a prime-minister giving birth and her partner staying home as the primary caregiver.
While many around the world would call this revolutionary, Clark wrote, in New Zealand this is simply "evolutionary".
"In my view, New Zealand is showing that no doors are closed to women, that having a baby while being prime minister can be managed, and that it's acceptable for male partners to be full-time carers. This is very positive role modelling for the empowerment of women and for gender equality."
