The previously wholly southern hemisphere rugby competition is expanding to 18 teams next season with sides in South Africa, Argentina and Japan joining the tournament.
Japan's Sunwolves side will play some of their home matches in Singapore.
The Chiefs will play the seven-time champion Canterbury Crusaders in Suva on July 1. It is only the second time a New Zealand side will play a home match outside of their country.
The Crusaders played a 'home' match against South Africa's Sharks in London in 2011 following a devastating earthquake that forced the team to play all of their games away from Christchurch that season.
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"This is a great opportunity to take the... Chiefs to Fiji and help promote the game in their country," Chiefs CEO Andrew Flexman said.
"Fijians have added a huge amount to New Zealand's rugby heritage and it is fitting that we can give something back as well as expose our brand in a new territory.
"We know how much the Pacific Island people love their rugby and this year's test match between Manu Samoa and the All Blacks was testament to that."
The Crusaders had investigated taking one of their home matches to Fiji during the 2015 season due to a scheduling clash with soccer's under-20 World Cup in New Zealand, but instead played the game against the Wellington Hurricanes in Nelson.
Crusaders winger Nemani Nadolo played for Fiji at the recent Rugby World Cup in England, while he will be joined by flyhalf Ben Volavola next season after Dan Carter, Colin Slade and Tom Taylor all signed European contracts.
(Reporting by Greg Stutchbury; Editing by John O'Brien)
