That was lower than their Australian peers - of 37,423 ICAA members who voted, 77.95 per cent were in favour.
The final voter turnout was also announced today, showing 61.5 per cent of ICAA and 58.7 per cent of NZICA members had chosen to cast their vote.
NZICA chairman Graham Crombie said the result provided a clear mandate for change.
"This proposal has been almost two years in the making and we've been discussing it with members for over a year. We're pleased that members on both sides of the Tasman have seen the benefits that forming a new institute together can produce."
ICAA president and chair Tim Gullifer said the new institute would give "the scale and strength we need on the world stage".
"It is fantastic that our members have had the foresight and the courage to do something very few professional bodies around the world have done and join together across borders to better serve their members."
Today's result was not welcomed by all, with Hamilton accountant Bruce Sparrow saying he was "gutted".
The fact that about 30 per cent of NZICA members voted against meant it was "not a resounding victory", he said.
Sparrow has been spokesman for a group of about 150 accountants who set up a website some months ago called 'Say No To One Institute'.
He said a 58.7 per cent voter turnout was "appalling" and that he believed the result could have been different if all NZICA members had voted.
"From the public practitioners I've been speaking to, we didn't see it (merging) as an advantage. But we've got to accept this decision."
Sparrow believed New Zealand and Australia were totally different countries in terms of taxation and politics, and merging the two made no sense.
There was also a fear of losing sovereignty to a much larger Australian body, which has 73,000 members compared to NZICA's 33,000.
Between May and July, NZICA and ICAA carried out eight weeks of consultation by holding face-to-face roadshows, webinars, accepting submissions and by polling members.
Implementation of the so-called One New Institute is expected to in April next year.