Existing public access and use rights would be unchanged, and third party rights including infrastructure, buildings and leases would continue.
Many of Auckland's most well-known volcanoes are part of the deal, including Mt Eden, Mt Hobson, Mt Wellington and Mt Victoria.
Mt Mangere will continue to be owned by the Crown but will fall under the co-governance model.
A spokesman for Mr Finlayson said the deal was "definitely a step towards a new tree'' on the summit of One Tree Hill.
The council has said it would not plant a new tree until Treaty issues were settled.
However, the deal still needs to be approved by local iwi and hapu before it is signed by the collective and the Crown and enacted in legislation.
The deal will also see four Auckland islands returned to Maori _ Rangitoto, Motutapu, Motuihe and conservation island Tiritiri Matangi.
The islands will then be returned to the Crown for the benefit of all New Zealanders after one month in manu whenua ownership, with the exception of the summit and two historic waka mooring sites on Rangitoto, which will remain in iwi ownership.
Brown's Island will continue to be owned by Auckland Council and managed by DoC.
Mr Finlayson said the settlement was a significant step forward for Auckland iwi and the wider community in putting past grievances behind and looking to the future.
"The wider Auckland region accounts for around a quarter of all remaining historical settlements, and is a complex area with many overlapping claims and shared interests,'' he said.
"This collective agreement represents a significant step forward in settling these important claims.''
The deed of settlement also gives collective members a first-right-of-refusal on Crown land being sold in the Auckland area.
It was initialled by Mr Finlayson and representatives of the collective, excluding Ngai Tai ki Tamaki, at the Auckland War Memorial Museum today.
Auckland Mayor Len Brown, whose council has been involved in the negotiations, was present.
Mr Brown hailed the deed of settlement as an historic move for Auckland and an important milestone for mana whenua.
"It should provide a firm base for settling individual treaty claims and for new opportunities, including economic development and cultural expression.
"The sharing of responsibilities should provide a different perspective on how we treat this important part of our city's heritage, going forwards.''
Mr Brown said the settlement would go a long way to securing the interests of generations to come in Auckland.
The iwi and hapu that make up the collective are Ngai Tai ki Tamaki, Ngati Maru, Ngati Paoa, Ngati Tamaoho, Ngati Tamatera, Ngati Te Ata, Ngati Whanaunga, Ngati Whatua o Kaipara, Ngati Whatua Orakei, Te Akitai, Te Kawerau a Maki, Te Patukirikiri and Te Runanga o Ngati Whatua.
