Stokes missed the entire series in Australia after being banned from international duties while police investigate his alleged role in a fight outside a nightclub in Bristol three months ago.
He kept his hand in by playing for Canterbury, his New Zealand birth province, for a month, but has since returned home to be with his wife and young family.
England selectors said he was in the frame “though his involvement remains subject to any relevant legal or disciplinary developments in relation to the incident in Bristol in September”.
Seamer Mark Wood returns after struggling with injury, and Ashes under performers Mooen Ali, James Vince and Mark Stoneman were all retained.
But Gary Ballance, Jake Ball and Tom Curran, who were all part of the Australia Test squad, miss out.
England play two Tests in New Zealand starting in Auckland on 22 March after being thrashed 4-0 by Australia in the Ashes series that ended in Sydney this week.
In the chastening campaign, Australia record four comprehensive wins including two innings victories and a 10-wicket triumph.
Livingstone was rewarded for his form with Lancashire, with National Selector James Whitaker saying they had been watching him for some time.
“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,” he said.
“He is a very talented and tough cricketer who has the ideal qualities and character to be successful in the Test arena.”
Selectors also recalled Durham seamer Wood, who is back in the Test 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,” said Whitaker
England – Joe Root (capt), Moeen Ali, James Anderson, Jonny Bairstow, Stuart Broad, Alaister Cook, Mason Crane, Ben Foakes, Liam Livingstone, Dawid Malan, Craig Overton, Ben Stokes, Mark Stoneman, James Vince, Chris Woakes, Mark Wood.