The 24-year-old Livingstone has not played test cricket but took part in two Twenty20 internationals against South Africa last year.
Fast bowler Mark Wood was also included after recovering from injury.
“Liam has been a player that we have been impressed with for quite some time, having performed well in the county system with Lancashire and over the past couple of years with the England Lions," National Selector James Whitaker said in an England and Wales Cricket Board statement on Wednesday.
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“He is a very talented and tough cricketer who has the ideal qualities and character to be successful in the test arena."
Wood, 27, was named in the squad for the first time since last year.
“After a frustrating period with injuries, Mark is now back to full fitness and is looking forward to being part of our test plans," Whitaker said.
All-rounder Ben Stokes was included, although he is still suspended by England and missed the recent Ashes series after being arrested in September on suspicion of causing actual bodily harm in an incident outside a Bristol nightclub.
Batsman Gary Ballance, fast bowler Jake Ball and all-rounder Tom Curran, who were all in the squad for the Ashes series which England lost 4-0, were left out.
“All three players have worked hard on the recent Ashes tour,” Whitaker said.
“Unfortunately, they miss out on selection for New Zealand. They are talented players and I am sure their time will come again.”
England squad - Joe Root (captain), Moeen Ali, James Anderson, Jonny Bairstow, Stuart Broad, Alastair Cook, Mason Crane, Ben Foakes, Liam Livingstone, Dawid Malan, Craig Overton, Ben Stokes, Mark Stoneman, James Vince, Chris Woakes, Mark Wood
(Reporting by Ed Osmond; Editing by Toby Davis)
