Demolition of the eyesore ABC building will begin next month, take around 12 weeks and be completed by the summer, the council has said.
The move is the first step towards the regeneration of the Kirkgate area, with around 90 new homes and extra car parking lined up to replace the ABC and other buildings that will be demolished.
The cinema first opened in 1935, but has stood empty for two decades before being purchased by the council in 2020.
Others however, including the London-based Cinema and Theatre Association claimed the "architectural quality" of the building meant it was worth saving.
The council has warned that noise and vibrations are likely to come from the works, and asked for "patience" from neighbours and the travelling public.
They said that the demolition will be designed to "minimise disruption."
Councillor Darren Byford, the authority's Cabinet member for regeneration, said: "This is not about bricks and mortar. People are at the heart of this transformation that will make residents feel prouder and safer in the place they call home, create a vibrant high street and have great connections that appeal to residents and visitors and build a fairer future for all.
“Though it is led by the council, which has secured millions of pounds in government funding, these plans are co-produced by residents and businesses who have shared their aspirations for a modernised city centre that stays in step with the trends across the UK to ensure city centres remain vibrant and attractive to all."
The council said some neighbouring properties, dating from the 1950s, will be demolished later this year having "reached the end of their lifespan".
The Harewood Arms pub will be among those that remain.
The council said that the overall site will then be put on the market for a developer to buy and then build the new homes.
Local Democracy Reporting Service