"Opportunities for economic, social and cultural development were lost, and tribal structures were weakened, as many had to leave their rohe altogether.
"Those who have remained now live in one of the most socially and economically deprived areas of New Zealand.
"Next week is the 40th anniversary of the start of the Dame Whina Cooper-led land march from Te Hapua to Wellington that protested the alienation of Maori land. This is a fitting time for the Te Hiku settlements to pass into New Zealand law," Mr Finlayson added.
"The government is committed to concluding Treaty settlements with all willing and able iwi, and this is a significant step towards that."
"The settlement legislation will also wind up the Aupouri Maori Trust Board, which has been experiencing some difficulties of late. Te Puni Kokiri is working with the board to support it through that transition. I am confident the new leadership in Te Runanga Nui o Te Aupuri will ensure good governance for the future of the Aupouri people."
Meanwhile, the Maori Party congratulated the Te Hiku iwi, and Te Kawerau a Maki, whose claims process was also completed on Wednesday.
Co-leader Te Ururoa Flavell paid tribute to those who began the Te Hiku claim 30 years ago, including the late Dame Whina Cooper and the late Hon Matiu Rata, and to all those who had carried the claim and the negotiations through to a final settlement.
"They have shown great tenacity and endurance," he said.
The Te Hiku settlement included recognition of their Te Hiku iwis' kaitiakitanga of Te Oneroa-a-Tohe (90 Mile Beach).