Scarborough Council has agreed the £3.91m cost to demolish the Futurist ahead of Friday's planning decision.
The council's cabinet approved the figure today (Tuesday), which came in under the £4 million that had been budgeted.
It will now enter into an agreement with Willmott Dixon to carry out the demolition, should the planning application for the methodology of its razing be approved on Friday.
There were some concerns raised by councillors Tony Randerson and Janet Jefferson that councillors had not seen detailed breakdowns of costs.
Cllr Mike Cockerill, the portfolio holder for harbours and major projects, said: "The important issue for me is that it has come in under budget."
Cllr Jefferson read out a number of questions regarding the costs and financial planning for the scheme.
She also expressed concerns about the "democracy" of the decision being taken as it was a previous version of the cabinet which made the decision to move ahead with the demolition of the Futurist.
Cllr Cockerill told Cllr Jefferson that as she had not submitted her questions prior to the meeting he could not answer them as he did not have all the information she required and would respond in writing.
Cllr Bill Chatt also hit out at those who thought the cabinet was voting to demolish the building.
He was speaking after Cllr Mark Vesey said the committee should not vote to demolish the building until the plans on what would replace it had been made public.
Cllr Vesey said: "It needs to be replaced with something that boosts the heritage of the town and what you are voting on today is to demolish it and replace it with a flat piece of tarmac.
"We haven't seen what will replace it."
Cllr Chatt responded: "The decision to demolish the Futurist was taken at a Full Council meeting. This is about the budget.
"The cabinet only saw [the cost breakdown] yesterday.
"I have seen no plans on what will replace it but does that stop us from making this decision today? I would say no.
"People out there are sick to death of it. The social media nightmare what runs with this is unbelievable.
"Whenever you see it it is like taking the top off a scab, it just brings everybody out and everybody just moans and groans. At the end of the day, we're trying to run an effective business, this has been going on since 1995."
Scarborough Council's planning committee will meet on Friday to decide on the method of demolition of the building.
The vote to demolish the Futurist was passed by a single vote in January.