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, and 6 batting spots and as cover for Anderson if he was to get injured.
He also noted that Elliott had previously played well in New Zealand and Australian conditions, was in good form, and offered 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.
"Some people are always going to miss out and I think we've got a good five."
Skipper Brendon 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 could adopt a "horses for courses" approach and adapt to different conditions, selectors said. "We probably won't roll out the same 11 every game," Hesson said.
He stressed the need to ensure every player was confident, fit and fresh for the start of the 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."
NZME.
