The biggest increases were from Australia, the United States, and China, said Statistics NZ.
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The Tourism Industry Association said the three million milestone was outstanding.
But even more importantly, international visitors are spending more than ever before, said TIA chief executive Chris Roberts.
Average spend per international visitor is up by 19 per cent and total spending is up by 28 per cent on the previous year.
The last full year figures to October last year show spending was $10.3 billion.
"The industry is aligned on its goal of maximising the spend of each and every visitor in order to reach the Tourism 2025 goal of growing total tourism revenue — domestic and international — to $41 billion a year," Roberts said.
Prime Minister and Tourism Minister John Key said he was "delighted" with the figures.
"Today, we have more people coming to New Zealand than ever, spending more and staying for longer, helping boost our economy and creating more jobs and opportunities for New Zealanders."
Key says New Zealand is benefiting hugely as a result.
Tourism was directly responsible for 94,100 jobs within the industry and supported a further 72,700 in the year to March 2014.
"Already, tourism is our second-largest export earner and the industry continues to go from strength to strength," he said.