The aluminium smelting plant has been a major employer on the island
Smelting operations at Anglesey Aluminium's plant in Holyhead will come to an end in September, leading to 390 job losses, it has been confirmed.
The firm said a viable solution could not be reached but last month rejected a £48m four-year aid offer because it was "not enough to break even".
The company had wanted an extension of its deal to buy electricity cheaply from nearby Wylfa power station.
Welsh Secretary Peter Hain said he was "bitterly disappointed" at the closure.
Gwilym Owen of the Unite union said: "This news is very disappointing after so much work and effort was put into keeping operations here. The most disappointing thing of all is that we were so close to getting an agreement."
Ynys Mon MP Albert Owen said the closure would be a "devastating blow to the region's economy".
Mr Hain added: "We put forward an extremely generous proposal in good faith which would have provided £48m financial assistance to the plant over the next four years.
David Bloor, managing director, said they fought to the last minute to save the deal
"We undertook a huge amount of detailed work in a very short time to put the..package together but it was simply not possible to reach an agreement."
In July, the company announced 250 redundancies, hot on the heels of 140 voluntary redundancies. Up to 80 other staff will be kept on to maintain the site.
In a statement, the company said there had been no breakthrough in its negotiations with the Nuclear Decommissioning Authority to try and extend its existing power contract.
It said the workforce "has been patient" over the "last-minute negotiations with governments that might have reversed or changed" the redundancy notices.
It added: "This notice today brings an end to that period of uncertainty."
Ieuan Wyn Jones, the island's AM, who is also economic development minister with the Welsh Assembly Government and leader of Plaid Cymru, called it "devastating news for the workforce and for the island's economy".
He said: "I am extremely disappointed that the company did not feel able to accept the offer of support on the terms set out."
A Welsh Assembly Government spokesperson said: "We have worked extremely hard to put a £48m rescue package together in conjunction with the UK government and it is unfortunate that the parent companies RTZ and Kaiser were not able to accept such an attractive offer.
"Our absolute priority now is to help the people involved to find alternative jobs - or to acquire the new skills needed for alternative careers.
"We are also working closely with the company and Anglesey County Council to examine all possible options for creating new employment opportunities on the Anglesey Aluminium site."
Anglesey council leader, Clive McGregor, said the news was a "huge blow not only for the workers at the smelter, but for the whole economy of Anglesey".
He said: "I would like to commend our colleagues in Westminster and Cardiff, and county council staff, for all their efforts over the past weeks and months.
"I am hugely disappointed that the company did not accept the generous offer that was on the table."
David Melding, the Welsh Conservatives' economy spokesman, said Anglesey Aluminium's decision was "regrettable".
He said: "This will be a great blow to the local economy and will be particularly harshly felt on Anglesey which has a narrow economic base and has been suffering during the recession due to its position as one of the poorest parts of Wales."
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