Chris Gayle was retained as captain while Ramnaresh Sarwan will be his deputy on the West Indies roster that will play Tests at Dunedin on December 11-15 and Napier on December 19-23 plus two Twenty20 and five one-day matches.
All-rounder Nash, who played for Jamaica in the West Indies tournament, had previously represented Queensland in Australia.
Lionel Barker, Kemar Roach and Leon Johnson were the other new faces on the West Indies squad.
Barker, from Montserrat, and Roach, from Barbados, are fast bowlers while Johnson is a batsman from Guyana.
West Indies coach John Dyson said players look forward to the tour and hope to move up in the world cricket rankings. The West Indies are eighth in the test rankings, one point below New Zealand.
"The New Zealand series will be hard fought," Dyson said. "New Zealand is ranked one place higher than us and a series win might see West Indies overtake New Zealand.
"Like all the top teams, we will be looking for strong performances from our experienced, senior players."
The Test squad for New Zealand is: Chris Gayle (Captain), Ramnaresh Sarwan (Vice Captain), Lionel Baker, Carlton Baugh, Sulieman Benn, Shivnarine Chanderpaul, Sewnarine Chattergoon, Fidel Edwards, Leon Johnson, Xavier Marshall, Brendan Nash, Daren Powell, Denesh Ramdin, Kemar Roach, Jerome Taylor.
The West Indies also named a one-day squad to face Pakistan in Abu Dhabi, with line-ups for the 20-20 and one-days in New Zealand to be named later.
The West Indies squad to play Pakistan will be: Chris Gayle (Captain), Ramnaresh Sarwan (Vice Captain), Lionel Baker, Carlton Baugh, Shivnarine Chanderpaul, Sewnarine Chattergoon, Shawn Findlay, Leon Johnson, Xavier Marshall, Nikita Miller, Dave Mohammed, Brendan Nash, Daren Powell, Kemar Roach, Jerome Taylor.