The gain in migrants last year was led by India, where an extra 4,599 arrivals took the total to 11,303 and saw the country overtake China as New Zealand's third-largest migrant country.
Australia was the second-largest source of migrants, cementing its position as New Zealand's largest source, with an extra 3,726 arrivals taking the total to 23,275.
An extra 1,333 migrants came from China, taking the total to 9,515, while an additional 1,230 arrivals from the Philippines took its total to 3,890, the sixth-largest.
Meanwhile some 258 fewer migrants arrived from the UK, the second-largest source of New Zealand's migrants, taking the total to 13,680.
A net 3,797 New Zealanders relocated to Australia in 2014, just a fifth of last year's net loss of 19,605 people and substantially down from 2012's net loss of 38,796, the agency said. It was the smallest net loss to Australia in a 12-month period since May 1994.
Still, for the December month net migration slowed to a seasonally adjusted gain of 4,100, the lowest level in seven months and down from 5,000 in November and a peak of 5,230 in October due to fewer arrivals of non-New Zealand citizens, the agency said.
"A monthly pace of net immigration of 4,100 is still very strong," Westpac Banking Corp senior economist Felix Delbruck said in a note.
"However, it is a significant drop from the recent monthly pace of around 5,000, and raises questions around whether the migration boom will continue to intensify. At this stage we are inclined to take the December drop with a grain of salt. Seasonal factors can make the underlying trend hard to gauge around this time of year."
Separately, the number of visitors to New Zealand rose 5 percent in December from the year earlier month to a record 402,500, as visitors from China surged 39 percent, the agency said.
China also contributed the biggest annual increase in visitors, followed by Australia, the US and Germany.
Total visitor numbers rose 5 percent in 2014 to 2.86 million, the agency said.
New Zealanders departures on overseas trips rose 4 percent to 2.27 million in 2014.