Maori will be able to make their claims through the courts or though direct negotiation with the Government.
If awarded title, they will receive a paper deed with title to a particular coastal area.
It will be a property right but they will not be able to exercise full ownership rights.
They will not be able to sell land or prevent public access.
But they will be able to exercise great control, such as vetoing development or initiating development, and permitting activities.
They will have the right to non-nationalised minerals beneath it, such as iron-sands.
Ngai Tahu leader Mark Solomon called it an ownership right but "inalienable" - unable to be sold.
Prime Minister John Key was insistent that only a small number of iwi and hapu would be successful in claiming customary title because they would have to show continuous and exclusive occupation of the relevant area since 1840.
The Foreshore and Seabed Act 2004 extinguished Maori rights to test customary title in the courts, following a Court of Appeal decision in 2002, and the Government asserted Crown ownership of the foreshore and seabed.
Mr Key said it was important for the nation to settle the issue "so it does not remain as a weeping sore that would have to be addressed at some stage by a future government".
The Government has also agreed to declare in law that Maori have mana over the foreshore and seabed.
The recognition will cite specific iwi and hapu with specific coastal areas, although more than one group will be able to have their historic association with an area recognised.
The new law will spell out to statutory organisations what rights recognised iwi and hapu have on conservation in their area, based on law and best practice.
The universal recognition or "mana tukuiho" was the main change that emerged yesterday after agreement between National, the Maori Party and the Iwi Leaders Group to repeal the Foreshore and Seabed Act.
The Government also agreed iwi that have already have a Treaty of Waitangi settlement, can make a new claim for customary title over the foreshore and seabed.
The National Government largely stood firm on the proposals it issued in March despite disagreement from the Maori Party and iwi group.
Maori groups opposed ownership being in the "public domain", wanting it vested jointly in Maori and the Crown, plus a lower threshold for iwi and hapu to claim customary title.
The new "mana tukuiho" - recognition for all iwi with a coastal connection, whether or not they meet the test for customary title seemed the sweetener that secured agreement yesterday, and the assurance that all coastal tribes, including those that have settled, could negotiate.
Attorney-general Chris Finlayson said the same test for customary title would apply to groups negotiating with Government as would do with the court.
Maori Party co-leader Pita Sharples described customary title as a "full-blooded title".
"...Maori regard it as a taonga tukuiho [a legacy] that it shouldn't be sold, that is built into it, but the question of public access has never been a question."
Dr Sharples also sought to reassure people that for many, nothing would change.
The Iwi Leadership Group yesterday congratulated the Maori Party yesterday, but not before a slight hiccup was resolved.
Mr Solomon took Dr Sharples aside and Waikato-Tainui chairman Tukuroirangi Morgan took Mr Finlayson aside straight after the press conference to seek an assurance that iwi with settled claims - including their own - would still be able to make customary title claims.
After getting the assurance it still stood, Mr Morgan said it would be an "extraordinary opportunity" and he would rather negotiate directly.
Mr Solomon said Ngai Tahu had 168 hapu and it would make sense for any claim to go through Te Runanga o Ngai Tahu.
Maori Party rebel MP Hone Harawira said last night the Prime Minister had chosen to "pander to the rednecks rather than give Maori the justice we deserve" and he wanted the foreshore and seabed vested in Maori title.
He said it was a pity Maori had not known three months ago that "public domain" was not negotiable and saved Maori "all the anguish and heightened expectation that has been created by this b... .... consultation process".
The Maori Party has won a major victory by achieving what it was created to do - repeal the Foreshore and Seabed Act, a University Of Otago academic says.
Dr Paerau Warbrick, of Te Tumu School of Maori, Pacific, and Indigenous Studies, said while the public would notice little change, one possible stumbling block was a move to have customary titles heard in the High Court rather than the Maori Land Court.
Dr Warbrick said the High Court process was expensive and complicated, and could penalise whanau and hapu, including those in Otago, with claims before the Maori Land Court.
"This will be the big question. It changes the goalpost."
- New Zealand Herald/additional reporting Hamish McNeilly