The expedition, named Waka Tapu, or Sacred Canoe, left Auckland in September and covered over 10,000 nautical miles on waka hourua, or two traditional sailing canoes - Te Aurere and Ngahiraka Mai Tawhiti.
Karl Johnstone, Director of the New Zealand Maori Arts and Crafts Institute, was in Easter Island, also known as Rapa Nui, for the arrival.
"Everybody's feeling very elated - it's been a long time at sea and obviously it's had its challenges," he's told Radio Australia.
"It has been longer than we initially predicted, but then when you're navigating by traditional systems there's no real telling how long it's going to take if you're at the mercy of the environment."
Mr Johnstone says the canoes had arrived a few days ago, but those involved and the community on Easter Island wanted to pay tribute to the man behind the mission, Master Builder Te Hekenukumai Busby.
"The wakas have been sitting out from the island for a few days now waiting to come ashore," he said.
"They've had to wait there while Hector Busby, who's the waka builder - he's the 80 year old whose vision this whole project has been for 20 years - so they've been sitting out there almost tormented, but not being able to come onshore, because it's really important from a protocol perspective that Hector be on board when they came in."
Map: Waka Tapu's planned journey
It's not known if the journey between New Zealand and Easter Island has been attempted before.
Mr Johnstone says it is the last remaining leg of the Polynesian Triangle - which stretches between Hawaii, Easter Islabd and New Zealand, to be conquered.
"[Hector's] vision has always been one of reconnecting Pacific cultures through the practice of waka, and I guess the remaining element that hadn't been completed in modern day times, for anyone in the Pacific, was the voyage between Rapa Nui and New Zealand," he said.
"For it to happen - he was very emotional. Two years ago I don't think he thought it was going to happen, or that it was very likely to happen, or was going to happen, and then all of a sudden we fell into the planning of this significant project."