Kane Williamson's side will then return to Australia in March for a one-day series with the opening two games in Sydney followed by the final match in Hobart.
Australia will also host a test series against Pakistan in November.
New Zealand last played an ODI on Australian soil in 2016 - a 3-0 series defeat. It's been 10 years since the Black Caps last beat Australia in an ODI in Australia.
Test Series v New Zealand
December 12-16: Perth Stadium, Day-Night test 1pm (6pm NZT)
December 26-30: MCG, 10.30am (12.30pm NZT)
January 3-7: SCG, 10.30am (12.30pm NZT)
ODI Series v New Zealand
March 13: SCG, 2.30pm (DN) (4.30pm NZT)
March 15: SCG, 10.30am (12.30pm NZT)
March 20: Blundstone Arena, Hobart, 2.30pm (DN) (4.30pm NZT)