"David has had a very big summer and will benefit from a break in cricket, both mentally and physically," interim national selector Trevor Hohns said Monday.
Vice-captain Warner was man-of-the-match against Pakistan in Sydney on Sunday when he hit 130 off 98 balls, his 12th one-day century.
Hohns praised Finch's return to form in the Twenty20 format.
"His form in the Big Bash League (BBL) has been very good and he has earned his recall," the selector said.
"I'm pretty comfortable with the changes that I've made. I'm also mentally in a better spot for the changes, and probably for being dropped.
"It gives you to time to reflect and analyse your game a little bit more in-depth than if you just roll from series to series," Finch said.
Western Australian batsman Shaun Marsh is the only other change to the one-day side that have already won the current one-day series against Pakistan 3-1 with a match left to play in Adelaide on Thursday.
"This provides Shaun with a chance to get back into international cricket following his injury earlier in the summer," Hohns added in a statement.
The squad will depart for New Zealand on Friday with Australia currently holding the one-day Chappell-Hadlee trophy after beating New Zealand 3-0 at home late last year.
The matches are in Auckland on January 30, Napier on February 2 and Hamilton on February 5.
Australia squad: Steve Smith (capt), Pat Cummins, Aaron Finch, James Faulkner, Peter Handscomb, Josh Hazlewood, Travis Head, Shaun Marsh, Glenn Maxwell, Mitchell Starc, Billy Stanlake, Marcus Stoinis, Matthew Wade, Adam Zampa.
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