The two main events to be held at Te Wharau, east of Masterton, are the Oceania Long Distance today and the Oceania Relays on Friday.
Both events will begin at 10am.
During both days there will also be a challenge between New Zealand and Australia, where each country will select three people to represent them at each of the age grades.
Mr Teahan describes orienteering as a "car rally on foot" and said it provides a challenge for all age groups competing with a compass and map.
"It's very important for New Zealand orienteering and to promote the sport to have the events here," said Mr Teahan.
"It's showing people of all ages what orienteering is all about and people can watch [the participants] competing and enjoying themselves."
The hosting of the World Cup and Oceania events has been supported by the Eastern and Central Community Trust who have given $8000 to help with event management.
On Tuesday, Wellington's Lizzie Ingham, 24, finished in third place at the sprint distance final for the World Cup at Manawatu.
This is the first time a New Zealander made the podium at an orienteering World Cup event.