The men - all aged over 18 - were brought into the country to work in the horticulture industry in the Nelson region in 2008-09, Peter Devoy, Immigration New Zealand's assistant general manager for compliance and border operations, said.
A tip-off in 2012 brought the case to INZ's attention, he said.
"I don't want to comment on the specifics but ... this is one of those cases where we did receive information and the investigation stemmed from that."
The trafficking charges were the first to be laid in New Zealand, he said.
"The elements of that require a person to come into New Zealand and require the elements of coercion or deception or both.
"Before we can bring a prosecution under that piece of legislation, we're required to go to the Solicitor-General for approval to prosecute.
"So it's a high-end charge, certainly for us, and there are a range of enforcement-type options available to us below this, especially under the Immigration Act, so it is significant that we've charged under the Crimes Act today."
He declined to go into the specifics of how the men were trafficked, the circumstances under which they were brought into the country, or the conditions they were living in when they were found, saying that "will be played out before the courts".
But he described it as "a generally unsatisfactory situation".
INZ is in contact with the 18 victims, some of whom are currently overseas, but others will remain here to give evidence against their alleged traffickers.
Mr Devoy would not say whether they would be deported or allowed to stay in the country following the court proceedings, but said there were "18 different sets of circumstances" and they would each be looked at individually.
The two men arrested in the Motueka area appeared in Nelson District Court today, where they were remanded on bail until September 4.
The man arrested in Auckland will also appear in Nelson District Court on September 4.
