"Council staff have met with the co-owner of the dogs and this person was remorseful of the situation, concerned for the victim and co-operative," a Wairoa District council statement said.
The co-owners now have 14 days to rehome their two other dogs that were not involved in the attack.
Another dog owner from the same address was also disqualified from owning a dog for five years as their dog was also not registered or contained and was found wandering.
Wairoa District Council chief executive Kitea Tipuna said this dog attack was particularly vicious and the injuries extreme.
He said it was regrettable these dogs were not contained and therefore able to inflict the serious injuries that they did.
"I am pleased the dog owners have been co-operative, taken responsibility and accepted the consequences of not having their dogs contained," Tipuna said.
"This dog attack serves as a reminder to our wider community and dog owners to please keep your dogs contained and under control to avoid this type of attack in the future."
Tipuna said the incident reinforces the need for dog owners to be responsible and follow the national guidelines around owning a dog, which includes registration and microchipping.
Wairoa mayor Craig Little said people who can't control their dogs should not have them.
"A dog like that should be locked up 24/7 as far as I am concerned," Little said.
On Friday that same week a child in Wairoa was hospitalised after being bitten on the hand by a family pet dog.
The dog responsible was impounded following the incident.