The record low marks a significant cut on the bank's other variable rate home loan, at 4.44%.
The product, "Blueprint to Build", will be available for borrowers for two years, from July 5.
Those building on the standard rate will receive a discount of 2.76%, while the offer is also available to those embarking on a new project.
ANZ will offer an additional sweetener to borrowers with a $3,000 cash contribution, as long as the home is 6+ Homestar rated.
The big four bank will contact customers in the coming days to restructure them onto lower terms, Ben Kelleher, the bank's managing director of personal banking, said.
"New Zealand’s fundamental problem is one of supply and demand. Making it more affordable for people to fund new builds is one way we can contribute to increasing supply in the market."
Kelleher said moves to force investors to raise their deposits had "taken some froth out of the market", and said the bank was keen to gear lending towards new builds.
"The 'Blueprint to Build' initiative is another step we’re taking to help more Kiwis on to the property ladder and to increase the stock of healthier homes."
ANZ's new build rate comes in cheaper than ASB's "Back My Build" rate at 1.79%. Both loans are significantly cheaper than the standard variable rates available to borrowers, with Kiwibank at 3.4% and the rest of the major banks above 4.4%.
Heartland Bank's online floating rate at 1.95% remains the cheapest available to all borrowers.