The bespectacled Vettori will lead New Zealand for the first time.
Regular skipper Stephen Fleming, who will lead the Kiwi side in the two Test series against Bangladesh will not be part of the ODI series as he is being rested.
Meanwhile, uncapped top-order batsman Peter Fulton has been included in the Kiwi One-day squad, while Australian-born former opener Mathew Sinclair is being recalled to the Test and one-day sides.
Tests: Stephen Fleming (captain), Mark Richardson, Mathew Sinclair, Scott Styris, Nathan Astle, Hamish Marshall, Jacob Oram, Brendon McCullum, Daniel Vettori, Paul Wiseman, James Franklin, Kyle Mills, Ian Butler, Chris Martin.
ODI's: Daniel Vettori (captain), Nathan Astle, Mathew Sinclair, Hamish Marshall, Peter Fulton, Scott Styris, Craig McMillan, Chris Cairns, Chris Harris, Brendon McCullum, Andre Adams, Kyle Mills, Ian Butler, one to be added.