The matches take place in Dunedin, Auckland and Wellington and Allardyce suggests it will be a great chance for the Hammers to widen their fan base down under.
"We've been busy putting together the best pre-season preparation that I've had, and it's great that we're able to go to New Zealand as a key part of that," Allardyce said.
"The tournament in New Zealand is particularly interesting, as it allows us to promote West Ham United and the Premier League over there.
"It'll be great for our fans in the region to see us play."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball