In a statement, Mr Hunt's family said they had lost a "much loved son and brother" in the tragic accident.
"We are grieving for this fine young man whom we will miss more than words can say."
Mr Saunders said family and staff had been offered counselling and other support as they began to work through their grief.
"We will endeavour to understand how and why this accident happened - this is our commitment to Junior's memory and his family."
He said the company would continue to work with authorities as investigations into the circumstances of the accident were carried out over the coming weeks.
Mr Hunt was pulled from the truck on Upton Terrace yesterday morning and taken to Wellington Hospital.
Mr Saunders said family members were with Mr Hunt this afternoon.
Three staff had taken time off work, including two who were his relatives.
"Another was one of our drivers on the scene and he's quite shaken by it all."
A local resident yesterday rang emergency services and then EnviroWaste. The driver who went to help was one of the first people on the scene.
WorkSafe New Zealand spokesman Julian Robins said the health and safety regulatory agency was investigating the incident.
EnviroWaste had a glass recycling contract with Wellington City Council.
