Sir Tumu said the report marked the end of a long journey to have his people's story formally acknowledged.
"We must now sit down with the Crown and explore how the original intentions of my great-great-grandfather can be put into effect."
He said iwi acknowledged that the mountains in the Tongariro National Park were precious and New Zealanders had nothing to fear with regard to access.
"Protecting the maunga for all New Zealanders in the appropriate way was the objective in 1887 and it remains the same today," he said.
The tribunal recommended the Crown should restore its partnership with iwi and the national park be made inalienable and held jointly under a new Treaty of Waitangi title.
It also recommended that the park be co-managed by a statutory authority comprising Crown and iwi representatives.