The Yorkshire opener was part of the tour to the West Indies, but did not play in the three-Test series with Jonathan Trott promoted to the top of the order alongside captain Alastair Cook.
But Trott has retired since the end of that series and 27-year-old Lyth is expected to get his chance after being one of the leading domestic run-scorers in England over the last two years.
The other 10 members of the team from the third Test in Barbados are all included in England’s squad with the only other addition being Durham pace bowler Mark Wood.
Wood made his senior England debut in the one-day international with Ireland last week, a match that was ruined by rain after he had secured his first wicket by bowling William Porterfield for seven.
Assistant coach Paul Farbrace will be in charge of the team while new director of cricket Andrew Strauss talks to candidates to take over from sacked coach Peter Moores.
The Test will be the 100th between England and New Zealand, the first having taken place in 1930.
National selector James Whitaker said: ???Adam has waited patiently for an opportunity with England having performed consistently for Yorkshire and England Lions in the last year.
“He fully deserves his chance to cement a place in the side at the top of the order. Mark has also impressed and his pace and style of bowling ensure the coach and captain have options in the bowling attack.??
???There were some positive signs during the recent Test tour and it is key that this group of players learns from the instances when the opposition was put under pressure and we were in a position to press for victory but couldn???t quite manage it.
“New Zealand are a very talented side and I expect a very competitive series between the two teams to start what will be an incredibly exciting summer of cricket. Good luck to Alastair, Paul Farbrace and the rest of the squad.???
England squad: Alastair Cook (captain), Joe Root (vice-captain), Ian Bell, Adam Lyth, Gary Ballance, Ben Stokes, Moeen Ali, Jos Buttler (wkt), Chris Jordan, Stuart Broad, James Anderson, Mark Wood.