Constable Hunt started with police as a member of Wing 312 in October 2017.
He spent most of his career working frontline at Orewa and Helensville Stations before recently moving to work in the Waitemata Road Policing Team based at Harbour Bridge Station.
Hunt was raised on the Hibiscus Coast by his mother Diane, with his sister Eleanor.
"It was his life-long dream to be a police officer," his family said in a statement.
Before joining the police, he completed a BA in criminology and worked at Auckland Prison as a case manager.
He also spent time living in the United Kingdom before he returned to New Zealand to join the police.
"Matthew was a person of great integrity," his family said.
"His closest friends were like his brothers and sisters and they along with his family are absolutely heartbroken by what has happened.
"He was passionate about sport and his physical fitness and was thrilled to enjoy the recent Blues game at Eden Park with his mates."
Police added: "Our priority remains on supporting his family at this tragic time."
They were also looking after the welfare of other police staff who attended the incident, including the other injured officer, as well as the injured member of the public.
"Our priority is to hold this offender to account," Coster told media.
"I ask that you keep this officer's family in your thoughts, as their loved one will not be coming home tonight."
Police Association President Chris Cahill also spoke out on the tragedy yesterday.
"We all know being a police officer is a risky job, but officers live with the expectation that they will go home at the end of their shift," he said.
"Their families live with that expectation too, and they have every right to see their loved ones home safely."
Cahill said the killing demonstrated risks to officers in "everyday routine policing" and highlighted the dangers of the "proliferation of firearms in the hands of criminals".
"It is an absolute tragedy that the very people who run towards danger to keep us all safe, can end up paying the ultimate price in the line of duty," he said.