A report released by Housing Minister Phil Twyford and the agency yesterday concluded about 800 tenancies suffered as a result of the testing regime used by Housing New Zealand (HNZ).
This included losing tenancies and possessions, being suspended from the waiting list, negative effects on credit ratings and being made homeless.
An HNZ spokesman said seven of these tenancies were based in Otago and Southland.
Mr Twyford said the agency was "committed" to redressing the hardship the tenants faced.
"This will be done on a case-by-case basis and the organisation will look to reimburse costs tenants incurred, and make discretionary grants to cover expenses such as moving costs and furniture replacement.
"They will also receive a formal apology from Housing NZ."
The agency was considering establishing a fund for affected tenants and their families to pay for addiction and rehabilitation services or other support.
The previous zero-tolerance approach was wrong and ignored many of the issues that put people into state houses in the first place, Mr Twyford said.
"Housing New Zealand failed, in some individual cases, to follow the principles of natural justice, by applying its suspension policy without providing sufficient detail to allow tenants to respond meaningfully to a notification that they were being considered for suspension."
The agency estimated each tenant would receive between $2500 and $3000.
HNZ chief executive Andrew McKenzie said the report showed the agency's previous approach had poor outcomes for tenants and their families.
"We plan to put things right and that means not just looking to rehouse those tenants who had their tenancies ended but to provide other forms of assistance," Mr McKenzie said
He estimated about 2400 people, from 800 tenancies, were ejected from state houses because of the policy.
It was a "shameful" number.
The former government should be held responsible for the "fiasco", he said.
The agency had been told by the previous government it should operate with a zero tolerance approach.
The agency adopted a new approach which put tenants at the heart of its work, Mr
Twyford said.
It was not clear whether anything could be done for other tenants who were dealt with through the Tenancy Tribunal, because the tribunal was part of the judiciary and the Government could not step in there.
Acting HNZ chairman Vui Mark Gosche said the board offered a heartfelt apology.
In May, the Prime Minister's then chief science adviser Sir Peter Gluckman produced a report which said there was no evidence third-hand exposure from methamphetamine smoking caused adverse health effects.
- Additional reporting NZME
