Mr Anderson (56), of Milton, was killed when the quad bike he was riding on a farm in Berwick Rd overturned, trapping him underneath about 6.45pm on Wednesday.
A relative, Steve Vickers, said the ''close-knit family'' were supporting each other at Mr Anderson's home in Milton.
''There's always an emptiness when you get something like this happen,'' he said.
''They are pretty devastated.
''Every passing is bad enough, no doubt, but a sudden one like this is terrible.''
Mr Anderson's three children paid tribute to their father on social media.
''A son's first hero, a daughter's first love. Nothing could ever prepare me for this. Rest in Peace Dad,'' his daughter wrote.
One of his sons said Mr Anderson died ''doing his lambing beat''.
''Missing you lots already mate. Till we meet again RIP xo,'' he wrote.
Mr Vickers described Mr Anderson as a good bloke who went out of his way to help his family.
''He always wanted to be a farmer. He trained as a carpenter and did a bit of shearing professionally.''
Mr Anderson returned to Milton in 2012 from Oamaru after his mother died the year before, Mr Vickers said.
''His mum and dad had lived in Milton all their lives and he was brought up here with his brother.''
Mr Anderson lived with one of his sons in his parents' former house, next door to his brother.
Farmer Murray Cullen, whose property Mr Anderson was working on when he died, offered his condolences to the family of his ''longtime friend and worker''.
WorkSafe New Zealand investigators removed the quad bike from the farm yesterday.
Contractors were used to lift the quad bike and an accompanying trailer off the farm.
An investigator told the Otago Daily Times he could make no comment other than that WorkSafe's investigation was ongoing.
Southern District Command Centre deployment co-ordinator Senior Sergeant Matt Scoles said the quad bike overturned while Mr Anderson was working on steep terrain on the farm.
The death was reported to the coroner.
Immediate family requested privacy yesterday.
