Quake Families Group spokesman Maan Alkaisi said he was "really very pleased" to see the significant step towards achieving justice.
"This is something we've been waiting for for around three and a half years.
"It's really quite an important and significant milestone."
Dr Alkaisi's wife Maysoon Abbas was killed when the CTV building pancaked during the magnitude 6.3 quake.
Other families felt the same as him, Dr Alkaisi said.
"They're really pleased that finally we can see at least some justice from accountability done.
"We always remember the 115 people who we lost there and they certainly deserve some justice."
The investigation was a lesson for everyone in the construction industry to put human safety and life in mind when they designed and built buildings, he said.
David Beaumont's son Matthew was killed in the tragedy.
He said he did not want "revenge" with the inquiry.
"I think already the truth is out there -- we know the faults were with the building."
There was a wide range of people and organisations which should be investigated, including the council and engineers who inspected the building.
"So it's not just one person and so I'll be very interested to see what comes out of this police investigation and how thorough it's going to be.
"All I want is for things to be better in the future."
Lawyer Nigel Hampton represented Srecko "Alec" Cvetanov, who lost his wife in the disaster.
He said Mr Cvetanov was "pleasantly surprised" that police were a step further forward in trying to hold someone accountable.
"But he remains realistic about the prospect of anything happening in the end."
For the families it had always been an issue of accountability and of someone standing up and accepting responsibility, Mr Hampton said.
"This is the only avenue left to them ... this police inquiry is their one remaining hope."That said, there is still a significant amount of work to be done before any investigation can be completed, the potential outcome of which is unknown."
Police had engaged the services of engineering consultants Beca to provide an expert opinion regarding the cause of the CTV building collapse.
The company would also provide expert opinion on whether there were any serious departures from accepted standards by those involved in the building's design or construction that could amount to gross negligence.
Police said interviewees for the inquiry would be contacted before the end of the year.