"The police's provisional information, as at February 13, 2020, shows that 61,332 newly prohibited firearms had been collected and destroyed, or modified by police-approved gunsmiths so that they comply with the new requirements and remain the property of their owners."
But neither police nor any other agency knew how many prohibited firearms, magazines, and parts were in the community when the law was changed.
"The previous regulatory regime focused on firearms owners instead of individual firearms. In part, because of this, the police do not have accurate information about how many firearms there are in the community.
"Without this information, we do not yet know how effective the scheme was."
The report found the police managed the scheme effectively, communicated well with the public, and that compensation payments did not exceed what was appropriate.
But it also found the administration costs for the scheme were more than expected.
In March last year, police produced an initial estimate of $18m to administer the scheme.
"The estimate was based on limited information from the Australian buyback scheme and was completed quickly, before the costs of the supporting technology were fully known," Ryan said.
"The police now estimate that, once fully completed, administering the scheme will have cost up to $35m. This includes costs of tracked staff time, contractors, and goods and services.
"This is nearly double the $18m the 2019 Budget provided and includes about $5.5m the police spent on the scheme in 2018/19."
The police used baseline funding from the General Crime Prevention Services appropriation to cover the excess administrative costs.
There was no evidence of "wasteful spending".
Meanwhile compensation of $102m has already been paid, and the final cost is forecast to be $120m.
The report recommends police continue to build relationships with firearms owners and dealers, improve the information they use to keep on top of gun regulations, and create a framework to show how the new regulations have made New Zealand safer.
That included taking steps to find out the level of compliance the scheme had achieved.
Police Minister Stuart Nash said the report was a "vote of confidence in police".
"We know we have more work to do to make New Zealand a safer place. We are bringing in a firearms register to better track guns in the community, and tougher penalties for gun crime."
Police have also seized more than 2400 unlawful firearms from gangs and other offenders since March last year.
"Police consistently warned we didn't have good information about exactly how many guns were in the community in the past. This is why we need a register, to enable police to better track firearms, to keep people safe and prevent crime."
National Party spokesman for police Brett Hudson said the report showed the scheme was not worth the amount of money spent on it.
"The Government has spent $103m on a buyback scheme it knew it would be unable to substantiate whether it was successful in making New Zealand safer. However, given police estimated there were 50,000 to 240,000 prohibited firearms in New Zealand, and only 57,716 firearms were handed in, it's clear which way this went," he said.
"Rather than tackling the real problems of unlawful possession and use of firearms, the Government pressed ahead with the buyback scheme, and millions of dollars later, no one can show that it's actually been successful."
ACT leader David Seymour also labelled the scheme a "disaster".
"ACT was the only political party to oppose the Arms Amendment Bill which set the framework for this scheme. We said at the time the gun buyback would not make New Zealanders safer. After a thorough investigation from the Auditor-General, that position has now been vindicated," he said.
He said the Government should drop its plans for a gun register and wait until the Royal Commission had reported before moving forward on further gun legislation.
In last year's Budget, more than $200m was allocated to fund the buyback scheme.
The Government moved swiftly to ban most semi-automatic assault rifles and certain high-capacity magazines after the Christchurch mosque attacks, which claimed 51 lives.
Police held 685 collection events across New Zealand from Stewart Island to Kaitaia, and went to more than 270 private homes to collect firearms.
Forty-three gun dealers also collected 6145 firearms on behalf of police.
