Across nine innings in England this summer, Guptill has tallied 167 runs at 20.87.
Fulton played 84 internationals for New Zealand from 2006 to 2014; he will join from August 1.
Craig McMillan feels the World Cup in England is going to be an open tournament and six to seven teams have a real chance of lifting the trophy.
A final call on Williamson and BJ Watling will be taken after Friday's training session in Christchurch.
McMillan said that whichever team won the toss would bowl first.
Williamson became the first New Zealander to 20 Test centuries as the hosts made 715/6.
New Zealand crossed 700 for the first time on their way to building a 481-run lead.
McMillan was given the role of batting mentor by former head coach Mike Hesson.
Williamson's 19th Test hundred increased to 67.65 his batting average in the second innings.
Former New Zealand batsman Craig McMillan has been roped in as the fielding coach.