Councillors voted 22 to 21 in favour of demolishing the South Bay building, costing the council Â£4million.
Cllr Bastiman, said: "It is a momentous decision for Scarborough because it will rid us of the eyesore which has been boarded up for the past three years.
"What is proposed for the new site will be an improvement and an attraction that will help keep Scarborough to the forefront of seaside entertainment.
"I am Scarborough born and bred and I am immensely proud of this town. I will be sorry to see The Futurist go, but it's not the most iconic of buildings now and we need to move on.
"I am pleased with the decision today and whatever goes on that site will be infinitely better than what stands there today."
Many speakers during the meeting at, Scarborough Town Hall, indicated they would be voting against demolishing the building.
Cllr Norman Murphy said: "The Futurist has great heritage, is nearly 100 years old and is unique. Why would we want to get rid of it? We will regret knocking the building down forever."
Cllr Colin Haddington said: "A total of Â£4million to demolish the Futurist shows a total disregard to the public purse. It should be down to the developer to absorb the cost of demolition."
Cllr Paul Cross said: "Not one of my constituents has come to me and said to knock The Futurist down. I believe we should have a referendum on the subject and let the people of the borough decide what the do with it."
However Independent Cllr William Chatt said: "The last show I went to see at The Futurist, there were nine people there. We have tried without success to obtain footfall figures during The Futurist's final three years in operation."
The council will now go ahead with plans to clear the site and stabilise a cliff behind the theatre to allow the land to be made available for redevelopment.
The Futurist, which has been closed since January 2014, will now make way for a new attraction, Flamingo Land Coast, to be built on the site.
Flamingo Land boss Gordon Gibb said: "Flamingo Land remains committed to helping the resort of Scarborough to achieve its full potential as a town, day visit location and holiday resort.
"We completely respect those who have an alternative opinion of what should be done with the Futurist site.
"Now that a decision has been made it is our hope that anyone with Scarborough's best interests at heart embrace this fantastic opportunity for the town."