Ardern's father Ross and mother Laurell said they were "very proud" of the new addition to their family - their third grandchild.
"We're a family that are fairly well grounded and to see this on the international media is absolutely different - I can say that without a shadow of a doubt," Ross Ardern told RNZ.
"But this is news that Jacinda wanted to share with New Zealand, and for it to be part of New Zealand, and I think her and Clarke have managed to do just that."
Ross Ardern said the baby girl would be good company for their other two grandchildren. He was part of the support team "as all members of our family will be".
Meanwhile, congratulations and parenting advice are flooding in from world leaders after the birth of Jacinda Ardern and Clarke Gayford's baby girl yesterday.
Canadian Prime Minister Justin Trudeau took to Twitter to welcome the couple to parenting, and offer tips to a fellow world leader.
"Welcome to the wonderful world of parenting @jacindaardern & Clarke," Trudeau said.
"Pro tip, Jacinda: Briefing notes make excellent bedtime stories."
The little girl - whose name has yet to be announced - was born at 4.45pm.
"Welcome to our village wee one," Ardern wrote on Instagram at 6.15pm on Thursday.
"Thank you so much for your best wishes and your kindness. We're all doing really well thanks to the wonderful team at Auckland City Hospital."
United Kingdom Prime Minister Theresa May was among the first to offer her congratulations.
"Congratulations to @JacindaArdern and @NZClarke on the birth of your little girl," she said.
Leader of the UK Labour Party Jeremy Corbyn also posted a heartfelt message to his New Zealand counterpart.
"Congratulations to New Zealand's Labour Prime Minister @JacindaArdern on giving birth to a baby girl," Corbyn said.
"It was a real pleasure to meet Jacinda with @EmilyThornberry in April in London.
"The whole of @UKLabour sends you our best wishes."
Australian leader of the opposition Bill Shortern was also quick off the mark.
"Wonderful news! Congrats @jacindaardern + @NZClarke," he said.
The daughter of former Pakistani Prime Minister Benazir Bhutto, who was the world's first modern head of government to give birth while in office, also took to social media to congratulate Ardern on the baby's arrival.
"Congratulations PM @jacindaardern on the birth of your daughter," Bakthawar B-Zardari said.
Ardern and Clarke's baby girl's birthday, June 21, is coincidentally the same as former PM Bhutto.
United States ambassador to New Zealand Scott Brown posted a congratulatory message in English and Māori.
"A warm welcome to the world. Wishing the family health, happiness, and all joy in the world. Tēnā koe i tō tamāhine. Ngā mihi mahana."
