Solo mum Anita Jones, 31, lives in the house and pays only $95 a week in rent.
She said she feels "privileged" to have her own home after sleeping for months on her brother's floor.
Ms Jones and her children, aged 14, 13, 6 and 2, moved into the house on January 18 just over a year ago after fleeing their previous state rental in Henderson to stay in a women's refuge.
Since then they have been staying with Ms Jones' mother, and then sleeping on the floor of Ms Jones' brother's home in West Harbour.
"There was no room for us, but he took us in anyway," she said.
"To be honest, without this house we would still be on my brother's floor. I'm privileged to be here."
Ms Jones said her state house was "in good condition", although she is rebuilding handrails on the front steps herself - "just tidying it up because it's really bushy".
The family had been on the social housing waiting list since late 2014 and were offered the Ponsonby house just after New Year.
"It's actually the best state house I've seen," she said.
"We love it because it's peaceful and it's not gang-related."
However she said Housing NZ had not given her any guarantee that she could stay long-term.
"They were just telling me that things might change in the future because people are trying to get this house," she said.
"They said they would relocate me if things change and we have to give up the house."
Housing NZ's 10 most valuable properties
1. Westmere: 3 bedrooms, 100sq m, $2.54 million.
2. Remuera: 3 bedrooms, 110sq m, $2.44 million.
3. Mangere East: 4 bedrooms, 98sq m, $2.33 million.
4. Remuera: 3 bedrooms, 98sq m, $1.96 million.
5. Remuera: 3 bedrooms, 90sq m, $1.96 million.
6. Ponsonby: 4 bedrooms, 150sq m, $1.96 million.
7. Ellerslie: 4 bedrooms, 100sq m, $1.91 million.
8. Orakei: 1 bedroom, 60sq m, $1.91 million.
9. Epsom: 2 bedrooms, 80sq m, $1.91 million.
10. Orakei: 2 bedrooms, 100sq m, $1.91 million.
Values from July 2015