Warwickshire opener Dominic Sibley is rewarded for his remarkable summer with a place on the plane alongside Kent batsman Zak Crawley and Lancashire duo Saqib Mahmood and Matt Parkinson.
Batsman Jason Roy is another to miss out after a difficult Ashes series while seamer James Anderson remains unavailable due to a calf injury.
Surrey batsman Ollie Pope is back involved and Jos Buttler will be the wicketkeeper in New Zealand due to Bairstow’s absence.
Mahmood and Parkinson are also in the Twenty20 squad for the five-match series, along with Somerset wicketkeeper-batsman Tom Banton and Worcestershire seamer Pat Brown.
Banton has burst onto the scene this season, hitting 549 runs in the Vitality Blast, while Brown took 17 wickets as Worcestershire reached the final at Edgbaston last weekend.
Mahmood and Parkinson helped Lancashire finish top of the North Group before their quarter-final exit, taking eight and 21 wickets respectively.
Eoin Morgan, who led England to 50-over World Cup glory earlier this summer, will also continue to captain the T20 side.
Stokes will cover regular captain Joe Root, who misses the first Test as he attends the birth of his second child.
Holder has led the West Indies for nearly five years.
Last month, Vikram Solanki took the reins at Surrey to become the only head coach among the 18 first-class counties from a diverse background.
A game-wide anti-discrimination charter and code will be introduced.
Stokes will be skipper for the first Test against the West Indies, and Root took the time to write a short note to his stand-in.
A majority vote was reached at a meeting of first-class counties chairmen on Tuesday.
The Durham man tiptoed around ICC rules on overt political statements but made clear the occasion would not go unmarked by England.
Contests between the two sides have seen a number of record-breaking performances.
The former England spinner insists Test cricket can survive a summer without crowds.
The pair will go head to head this week when the first Test between England and West Indies gets under way in Southampton.