The expedition's chief navigator is Tauranga's Jack Thatcher. He said it was fitting Mr Busby should be aboard.
"The people of Rapanui have huge admiration for Hector. He has contributed to waka culture across the Pacific including building many waka and generously passed on his navigational knowledge to others.
"The fact that he was here today to see his dream of closing the Polynesian Triangle come true was a special moment for all of us."
Mr Thatcher said it was an emotional ceremony as many crew members were reunited with loved ones who had travelled from New Zealand for the historic occasion.
"It's been a long four months of hard physical work and the journey has certainly changed our perspectives on life," he said. "It's an experience none of us will ever forget."
Mr Thatcher said Waka Tapu had re-strengthened the links between Maori and Rapanui. Following an exchange of cultural gifts, historically significant 'eyes' were temporarily placed inside Rapanui's famous Moai statues to symbolise cultural and human life. The act had not been performed for at least 100 years.
In reaching Rapanui, the crew members have used traditional navigational methods such as the stars, moon, sun, ocean currents, birds and marine life. The journey is recreating those made by the crew's Maori ancestors hundreds of years ago to reach Aotearoa.
The canoes left Auckland on August 17. They had intended to return to New Zealand by Christmas but bad weather played havoc with those plans.
Five Tauranga residents have taken part on the Auckland to Rapanui leg: Jack Thatcher, Kiharoa Nuku, Mahara Nicholas, Ani Black and Kushla Allen.
Three others, Tekuka Tukaokao, Tamahau Tangitu and Parerawhiti Taikato flew out to Rapanui, via Chile, as replacement crew members for the return journey.
Mr Tukaokao, a 31-year-old who teaches Te Reo at Te Wananga o Aotearoa, said he was excited to be joining the trip and saw it as a huge honour.
"It will be something to tell the mokopuna [grandchildren] when I get old that's for sure," he said.
By reaching Rapanui, the expedition has achieved its goal of closing the final corner of the Polynesian Triangle.
That triangle is defined by Hawaii in the north, New Zealand in the south and Rapanui in the east.
The Waka Tapu crew will spend a week resting before travelling on to Tahiti where the waka will lay over for the cyclone season.
Most of the crew will fly home to New Zealand and then return around April to sail the return journey back to Auckland.
Track the expedition's progress here.
