Newcastle will play Sydney in Dunedin on July 22, with Wellington taking on West Ham in Auckland the following day.
The tournament finishes with a double header in Wellington on July 26 when Sydney play West Ham and Wellington take on Newcastle.
Hammers defender Winston Reid, captain of the New Zealand national team, said he was looking forward to touring his homeland.
"Football is really on the up in both New Zealand and Australia and we are all looking forward to meeting all the fans and playing exciting matches against two leading A-League clubs," he said.
West Ham manager Sam 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."