It's been revealed the baby was wearing a hat knitted by a supporter, and a baby shawl knitted by Clarke Gayford's mum, in the photo that went around the world yesterday.
The Prime Minister's office says Ngai Tahu has also gifted the baby a blanket, which can be seen in the photo and which she is wrapped in today.
They say everyone is happy and well, and in a normal room on the maternity ward - where they moved to from the delivery suite, at about eight last night.
A Te Runanga o Ngai Tahu spokeswoman said members of the iwi met with Ardern earlier this year where kaiwhakahaere Lisa Tumahai, deputy kaiwhakahaere, Matapura Ellison and CEO Arihia Bennett gave gifts to the prime minister.
The items included clothing, a muslin wrap, a merino blanket and a piece of pounamu, she said.
"We believe the merino blanket the Prime Minister has in her hand in the Instagram photo is the one we gifted her."
Deputy kaiwhakahaere Matapura Ellison, who was one of the people to present the gifts to Ardern, was born and raised in Karitane.
Like a lot of dads, Clarke Gayford stayed the night in the room.
The family are planning to stay there for another night at least.
Ardern had little sleep last night, after celebrating her daughter's birth late yesterday afternoon with a dinner of Marmite toast and Milo last night.
Nurses said Gayford and Ardern's little girl was "very alert and one hungry baby".
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".
Gayford's sister, Briar Fraser told the New Zealand Herald they were all very excited about the arrival of the new family member.
"A wee girl evens up the numbers on our side as I have three boys and our sister has two girls," she said.
"My youngest, Hughey, is just 6 months old so it's going to be special having them grow up together."
Ardern's big sister, Louise Ardern, was also excited to welcome a new playmate for her daughter.
Louise Ardern famously gave birth to a baby boy while her sister was being sworn in as the 40th Prime Minister of New Zealand.
"I'm so excited to be an Aunty and can't wait to have cuddles. Based on what I've heard so far she seems very alert - just like my daughter Isabella who is very excited to have a baby cousin," she said.
Former prime minister Helen Clark says the birth is sending a "very powerful" statement to the world on gender equality.
"People are really interested in this first family and the statements they are making about gender equality and choice, Clark told Newstalk ZB.
"It has generated huge news internationally, because it is so uncommon for a serving prime minister to give birth."
"Young women are very excited about it because, in a sense, it validates their desire to have both a career and a family."
Gayford, who has said he would a stay-at-home dad, was also sending a strong message it was acceptable for male partners to be fulltime carers.
"For gender equality and women choosing their own destiny, the symbolism is very powerful," Clark said.
Among the hordes of wellwishes Ardern and Gayford have received is a private message from the Queen, whom she met this year on a trip to Britain.
