Young paceman Adam Milne is also there, while the other all rounder is Corey Anderson.
Veteran spinner Daniel Vettori is named in the squad but is expected to play a back up role to offspinner Nathan McCullum.
Hesson said Elliott was picked for his ability to cover the 4, 5, 6 batting spots in the middle order and as cover for Anderson if he was to get injured.
He also noted that Elliott has previously played well in New Zealand and Australian conditions, is in good form, and offers a bowling option.
"He's got a bit of craft about him."
Hesson said he delivered the message to Neesham and said that every player in the initial squad of 30 who didn't make the cut would be "extremely disappointed".
The decision to not select Henry was a "tough call", Hesson admitted, as there were six bowlers who have performed well recently.
It came down to a decision on the balance of the squad, he said.
The bowling stocks offered genuine pace, swing, craft, and experience, Hesson said.
"Some people are always going to miss out and i think we've got a good five."
McCullum said it was the strongest New Zealand team he's ever been a part of heading into a world cup.
The squad meant the team has the ability to adopt a "horses for courses" approach and adapt to different conditions, the selectors said.
"We probably won't roll out the same 11 every game," Hesson said.
Hesson stressed the need to ensure every player was confident, fit and fresh for the start of the February-March tournament.
McCullum said the squad would be well placed to cope with the pressures of playing in their own backyard.
"The guys are very humble and level with their emotions and that helps with the pressures."
The full squad is:
Brendon McCullum, captain
Corey Anderson
Trent Boult
Grant Elliott
Martin Guptill
Tom Latham
Mitchell McClenaghan
Nathan McCullum
Kyle Mills
Adam Milne
Luke Ronchi
Tim Southee
Ross Taylor
Daniel Vettori
Kane Williamson
