The court handed down its decision just after 9:30 a.m. Tuesday.
On Friday, a Superior Court judge gave the building’s owners the green light to demolish the building Little Burgundy.
The borough then took the matter to the Court of Appeal.
In May 2014, the centre's administration filed for bankruptcy, weeks after a wall in the historic building collapsed.
The centre said it was too expensive to repair the abandoned building on Coursol Street, leaving the organization no choice but to file for bankruptcy protection.
Court documents show the building is owned by a numbered company registered in Quebec.