"While Dad was physically healthy, he did suffer from some mental confusion and we feared he had fallen or lost his way in the bush," he said.
"Dad was a highly intelligent engineer and a well respected member of the community."
Stafford Smith said the family was pleased to be able to finally lay him to rest, and would hold a private cremation.
Police said a significant search operation was conducted when Mr Smith went missing in 1986, with about 70 staff and volunteers.
The case was referred to the coroner, and a finding was made that Mr Smith died on or about March 20, 1986.
On February 15 this year, a member of the public found the remains in a gully near Captain Edward Daniel Drive in Ngaio.
DNA results last week confirmed Mr Smith's identity.
Police said there were no signs of foul play or trauma, but the cause of death remained unknown.
Wellington City Area Commander Chris Bensemann said police were happy to finally be able to bring some closure to Mr Smith's family.
"His family have endured nearly 30 years of uncertainty since his disappearance, but the DNA results received last week mean they are finally able to get some closure."
His family have released a statement:
Statement from Stafford Smith (John's son) on behalf of the Smith family:
"Finding Dad's remains bring closure for our family.
Dad loved walking and regularly walked in bush around the Ngaio area.
While Dad was physically healthy, he did suffer from some mental confusion and we feared he had fallen or lost his way in the bush.
Dad was a highly intelligent engineer and a well respected member of the community.
He was a much-loved husband, father and grandfather and it's sad he died alone.
We are pleased we can now lay him to rest.
There will be a private cremation and we will have a family service for him later.
The family would like to thank the police for their support at the time he went missing and now, since he was found in February."
