Stokes, 26, hasn't played for England since an incident outside a Bristol nightclub past year, that resulted in an alleged assault, with the all-rounder stood down for the recently concluded Ashes series as a result.
"Last summer, I had a taste of what it's like to play for England but Test cricket is the pinnacle of the game".
Both Vince and Stoneman averaged under 30 with the bat in Australia against an admittedly high-class four-man bowling attack.
Liam Livingstone said, "It is a huge honour to have been named in the England Test squad for the first time".
Known for his hard hitting and a wide repertoire of strokes, Livingstone enjoyed some notable moments of success in 2017, in particular his maiden List A hundred - a blistering knock of 129 from 83 balls for England Lions against South Africa A at Northampton - and a career-best 224 for Lancashire against Warwickshire in the Championship in September.
"He is a very talented and tough cricketer who has the ideal qualities and character to be successful in the Test arena", he added.
"Mark is now back to full fitness and is looking forward to being part of our Test plans".
"Unfortunately, they miss out on selection for New Zealand". A decision as to whether Stokes will be charged is expected by the Criminal Prosecution Service soon.
Trevor Bayliss made a strong case for the retention of Mark Stoneman and James Vince when reviewing the campaign earlier this week, but the pair underperformed Down Under and there is little doubt that this show of faith requires immediate payback if they are to linger in the side.
The 24-year-old has already played two Twenty20 Internationals for England but is yet to make an appearance in the other two formats.
The ECB has confirmed that if they receive notification that Stokes has either been charged or not charged, the ECB board will convene within 48 hours to decide on his availability for the tour. Ball played in the first match at the Gabba and then was not seen again while Curran, a late call-up, was ineffectual in his two Tests at the MCG and SCG.
England dropped Ashes trio of Gary Ballance, Jake Ball and Tom Curran while including paceman Mark Wood and uncapped batsman Liam Livingstone for the two-Test tour of New Zealand in March.
The first test, starting on March 22 in Auckland, is a day-nighter.