The 42-year-old former New Zealand Warriors coach will be the right-hand man to Stephen Kearney at the tournament in the United Kingdom and France in October and November.
Kearney said: "Ivan understands our culture and is respected by the players. He is experienced as a coach and, importantly, he's match-fit. Those he has worked with closely have a lot of confidence in him."
Former Wigan centre Tony Iro, who is Cleary's assistant at the Warriors, will continue in his role as Kiwis' team manager for the World Cup.