The government estimated that about 2400 people from 800 tenancies had been wrongly kicked out of their state houses because of a zero tolerance policy.
A Housing New Zealand report in September acknowledged the approach had had a far-reaching effect on tenants, including losing their tenancies, their possessions, being suspended from the waiting list, poor credit ratings and being made homeless.
It found 542 tenants were charged nearly $7 million in total for meth contamination between 2013 and 2018.
Housing and Urban Development Minister Phil Twyford said the first 55 people were being paid from today - an average of about $8000 each.
Another 92 people have had claims approved and were waiting on an offer to be finalised.
Mr Twyford told Morning Report the formula for payouts was made on a case-by-case basis to cover expenses such as moving costs and furniture replacement.
"We're going to do our best to put this right. This was a debacle over a number of years," he said.
"A lot of people got hurt. Housing New Zealand is doing its best to track people down and make sure, if they're eligible, people get the assistance they deserve.
"This was a huge failure across government at multiple levels. I can't underline how much regret we feel for people who were hurt in this process."
Each affected tenant has also received a formal apology from Housing New Zealand, Mr Twyford said.
Mr Twyford said that in some cases, evicted tenants were made homeless and had to stay in hotels and motels were the Ministry of Social Development racked the expenses up as debt.
Housing officials have so far contacted almost 300 people about compensation - they earlier estimated about 800 would be eligible. There is not cut off time for claims.
Mr Twyford said he urged anyone affected to come forward to Housing New Zealand.
