Hesson said Elliott - who has won 51 ODI caps and last played in 2013 - got the nod over Neesham for his ability to cover the 4, 5, 6 batting spots in the middle order and as cover for fellow all-rounder Corey 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.
Elliott says he has a lot to offer with the bat in the middle order, and also with the ball.
"I really enjoy my bowling, I think it complements my batting nicely, it gets me in the game early.
"Maybe 5-8 overs ... if things are going well, I might get my 10 in ..."
The Wellington Firebirds skipper also believes his experience will benefit Brendon McCullum's team.
"I've played [51] games for New Zealand at one-day level and gone through a lot of culture changes, a lot of teams, played with lots of guys, in different conditions, and pressure-wise once you get older you've seen a lot of different scenarios.
"So hopefully the scenarios that I see in the World Cup I can rectify them and help to change those to swing them in our favour."
The 1992 tournament, hosted in New Zealand and Australia, was South Africa's first.
It made a "massive impression" on a young Elliott.
"After that I wanted to become a professional cricketer and I wanted to play at an international level."
When McCullum gave up the gloves in 2013, it meant that the No5 batting spot that Elliott had occupied was no longer available.
But Elliott says he never stopped chasing a recall.
He attributes his recent good form in the domestic game to "the enjoyment factor".
"You want to play for your country for as long as possible but selection is not something you can control," he said.
"You just have to try and enjoy your cricket, that's the main thing.
"But I want to be playing at the highest level. That's something I've always strived for, more so in white ball cricket for me.
"When you're young and playing for the Black Caps you start setting high expectations for yourself, high goals, and now it's just about enjoying every game that I play and bringing that enthusiasm that I first had when I started playing the game."