The recovery visa, brought in to help with the clean-up from Cyclone Gabrielle and Auckland floods, has attracted 400 applicants.
The government announced the six month visa less than three weeks ago, saying overseas specialists were needed to support the recovery efforts.
A total of 166 visas have been issued, with only two declines.
Immigration New Zealand general manager Richard Owen said applications were being prioritised and the average visa processing time was three days.
"So far 29 people whose applications have been approved have arrived in New Zealand. It's important to note that it takes time for people to arrange their travel to New Zealand and this number is expected to increase over the coming days and weeks.
"In addition, 66 applications for a specific purpose work visa similar to the recovery visa were received before 24 February. All of these applications have been processed and approved.
"There was no specific forecast of the number of people expected to apply for the recovery visa, but we are pleased with the level of interest as every single extra worker is contributing to the response to the recent extreme weather events."
The top occupations so far were building labourers (92) and commercial and domestic cleaners (41 and 37). Source: Radio New Zealand