Ardern delivered her 3.31 kg (7.3 lb) daughter in the country's largest public hospital on Thursday afternoon with her partner, television presenter Clarke Gayford, at her side.
All the presents for baby Neve would be passed on to another family once they had been used, Ms Ardern said.
Mr Gayford, known in New Zealand as the "first bloke", is the presenter of a fishing show, and Ms Ardern was the youngest New Zealand PM in 150 years, but she said they would not put pressure on their new baby.
"Also, it means - in various forms - it means bright and radiant, and snow which seemed like a good combination for Matariki (the Maori New Year) and for solstice". "Sleep deprived, but really well!"
"I do not want to create a false impression that all women should be super-human or super-women", she said recently.
"Those moments have mattered as much to us as any of those lovely messages of support from around the world", she said.
She answered a few questions from reporters while holding her baby at Auckland City Hospital before she planned on returning home.
Adern, glowing with motherhood, said it was a pleasure to finally introduce their little one to New Zealand and shared the chosen name for the first time since the birth.
"Over the next six weeks we'll do what every other parent does and learn the little nuisances ... and just figure things out as we go".
After the birth Ardern thanked everyone for their best wishes and kindness and said they were all doing really well thanks to the wonderful team at Auckland City Hospital.
"Seeing that person in the act, and then sending something to us, was absolutely handsome so those moments have mattered as much to us as any of those lovely messages of support from around the world".
She and Mr Gayford had opted to spell the name Neve - as opposed to Niamh for example - for simplicity, with Ms Ardern joking about the unusual spellings of Clarke and Jacinda.
Although she will become the first elected world leader to take maternity leave - and only the second to have a child while in office - Ms Ardern has played down the significant global attention she's received as a role model.
Ardern, 37, became New Zealand's youngest prime minister when she took office through a coalition deal a year ago after an inconclusive election.
After fronting the media, the Prime Minister then went back to her hospital room where she then addressed the public via a live video on her Facebook page.
Support also flooded in from around the world, with Britain's Queen Elizabeth, whom Ardern met in London in April, sending an emailed message of congratulations and Canadian Prime Minister Justin Trudeau tweeting at Ardern: "Pro tip, Jacinda: Briefing notes make excellent bed time stories".
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