Jacinda Ardern's parents Ross and Laurell Ardern have spoken to media.
The couple said Clarke Gayford has been reading up on parenting and will make a great stay-at-home dad.
"He's so easy-going, I'm sure he'll manage."
Laurell Ardern said the photos of the new baby showed how alert she was.
"In one of the photos she was looking up at Jacinda, and looked just in awe of her."
Ross Ardern said the Ardern family was a bit of a village and both the Arderns and Gayfords expect to be involved grandparents ready to help out whenever they can.
"The best advice I ever had was from my mother, just work hard and never give up. And that's the best advice for any parents."
The new baby will have a playmate for life with one cousin being 7-months-old.
Laurell Ardern said she has met women who told her of the Prime Minister's example on how women can manage a job and a newborn baby.
"I had one woman come up to me and tell me she was offered a job, but she thought it would be too hard, but then she thought 'well if Jacinda can do it, I can do it'."
Ross Ardern said the main advice he had for the new parents was: "Get plenty of sleep, look out for each other and take care of each other.
"We are certainly full of pride and joy for this child. We know that in Jacinda and Clarke's hands our new grandchild will have a tremendous future."
Laurell Ardern will be flying to Auckland tomorrow to meet the new baby. She was able to speak to Jacinda over the phone.
"She sounded very relaxed and excited, it was neat.
"I'm dying to see her and hold her, and see what she's like."