The first Test will be played here from February 6, while the second will be played in Wellington from February 14.
The most notable name missing was that of Martin Guptill, who struck his fifth ODI century in the tied third match against India here yesterday.
"It was a relatively an easy squad to select and is a just reward for players who have done well recently in this format. Guptill was discussed, but we are showing faith in Hamish Rutherford and Peter Fulton. Both of them did well in the last Test at Eden Park," said coach Mike Hesson, who also sits on the New Zealand selection panel.
"Jesse is playing well and he has had a good ODI series. But there is no spot in the playing eleven at the moment. Even Trent Boult will be fit and knocking soon, and that is a good position for us to be in, but there is no spot at the moment.
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"We have a pretty clear blue-print of what we like to do with Corey Anderson doing his job at number six and is also a bowling option as well," said Hesson.
"Ish has been doing well and he has bowled consistently. He is the best spinner in the country at the moment and he is only 21 years old. So that is a bonus," said the coach.
Two members of the Test squad, Fulton and Rutherford, will also feature in the New Zealand XI side that will take on India in a two day warm-up match game at the Cobham Oval in Whangarei on February 2-3.
New Zealand XI: Peter Fulton (c), Roald Badenhorst, Jono Boult, Anton Devcich, Tipene Friday, Jono Hickey, Shawn Hicks, Iain McPeake, Hamish Rutherford, Tim Seifert (w), Ill Tugaga, Henry Walsh.