The other sides of the triangle - from Aotearoa to Hawaii, and Hawaii to Rapanui - have already been sailed.
The waka made only two stops during the voyage, at Tubuai and Mangareva, both in French Polynesia.
Captain of Ngahiraka Mai Tawhiti, Jack Thatcher, said the crew had just dropped the anchor off the Northern end of Rapanui, just outside of Hanga Tetenga.
While there hadn't been too many "untoward happenings" on Ngahiraka, Te Aurere - which was the older of the two waka - had suffered a spate of broken paddles, Mr Thatcher said.
"They've had a pretty harrowing time. They broke three paddles on the way up to Tubuai and had to basically scavenge materials from the waka to repair the paddles.
"They were a carrying a spare one which they ended up having to use, but they broke that one as well."
The paddles were used "24/7" to steer the waka, Mr Thatcher said.
The hardest part of the voyage was the isolation and handling challenges with a "relatively new crew," he said.
"We went through four low [weather] systems, two of them were pretty bad.
"Encouraging people to keep at it during those times when it became really hard is probably the biggest challenge."
Mr Thatcher said his crew had grown hugely over the voyage and would come back "different people".
Memorable sights along the voyage included up-close visits from whales - the most impressive consisting of three pods of killer whales chasing a lone whale before arriving in Mangareva.
"We think they got it because we saw them jumping and all sorts out of the water. We're not too sure what it was, but it was a fairly sizeable whale."
While frozen meat was carried at the beginning of each stage, the crews diets were also substituted with tinned food, rice, bread which was made on-board and fish they caught on their travels.
"We've caught a number of different types of tuna and mahi-mahi and a wahoo."
The two waka tried to sail together, although there were times when the boats ended up as far as 30 miles apart, Mr Thatcher said.
Satellite phones and VHF radios were then used to communicate. "We try to keep in sight of each other."
Mr Thatcher said he was looking forward to the ceremony tomorrow where the Waka Tapu would be welcomed onto Rapanui.
The ceremony would be a cumulation of the four-month journey as the tapu would be lifted off Te Aurere - the waka consecrated for the voyage.
Ngahiraka was seen more as a support vessel on the voyage, and "didn't carry any tapu as such" he said.
Te Aurere was crewed by only men, while the crew on Ngahiraka were made up of both men and women. Ten people were on-board each, Mr Thatcher said.
The voyagers are planning on staying on the island until next week, then it's "back home via Tahiti".
Mr Thatcher said he missed his family and was looking forward seeing his wife and one of his daughters who had flown to Rapanui tomorrow.
