Celtica closed in 2006 after a ten year run as a Celtic expecience theme park based Machynlleth, a town and the former capital of Wales in Powys.
"The board of Powys County Council, which owns Celtica, voted to shut the centre at a meeting on Tuesday.
Celtica, which employs 14 people, was opened in 1996 after £2.5m was spent on refurbishing the Grade II-listed Plas building where it is based.
Last month, a campaign to save the attraction was launched.
Powys Council said a report by consultants showed Celtica had lost £1.1m since 1998 and was attracting too few visitors.
CELTICA REPORT
"Celtica is not fulfilling its strategic role as a major national and international visitor attraction"
"Its role has become distinctly local...somewhat at odds with its tourist attraction role"
"The mathematics of sustaining the attraction on that number of visitors does not lead to anything except a continuing high expenditure on the part of the council"
Source: KPMG report for Powys council
Earlier this year, the council's board was told it could not use money from a charitable fund - the Plas Machynlleth Endowment Fund - to pay for £250,000 in improvements at the attraction.
Board chairman Michael Jones said Tuesday's decision was made "with regret".
"The council, with professional help, has explored a huge range of options, but we now have no choice but to close Celtica," he said.
"Unless external organisations find £250,000 of capital investment by December 2005, the attraction will close at the end of the tourism season.
"Celtica has operated at a loss since it opened and it is not financially viable. Since its transfer to Powys in 1998 it has needed more than £1.1m in support."
Mr Jones said there would be "job losses in the immediate future" but said alternative uses for the building were being sought.
Celtica gave visitors an insight into how the ancient Celts lived
The decision by the Powys council's executive board will now go for final approval to the full council.
Peter Jones said he was very disappointed at the news, and added that the last few weeks had been "quite devastating for all involved".
The head of the Save Celtica Campaign, Machynlleth's mayor Bob Dunn, had wanted Tuesday's meeting halted so it could hold talks over its future.
"I am totally disappointed and disgusted," he said.
"It means yet another service is lost to Machynlleth - there will be a heck of a knock-on effect."
Beforehand, local AM Glyn Davies said councillors faced tough decisions to balance their books but hoped they would "think long and hard before finally pulling the plug on an attraction that puts Machynlleth on the map".
Celtica was established by the old Montgomeryshire District Council in 1995, and £2.5m was spent on refurbishing its Georgian home.
It needed 90,000 visitors in the first year with the figure increasing to 110,000 for it to be successful.
However, the council said Celtica had never attracted more than 34,000 visitors per year."
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