Andrew Cowie Construction will begin immediately on the listed building, which dates back to 1933, for a 2015 completion.
Over the next 18 months, the landmark building will be redeveloped to create 70,000 sq ft of office space.
Fairhurst are consulting engineers for the project, which was designed by Perthshire architect Keppie Design.
James Barrack, director of Knight Property Group, said: “Now, we can look forward to restoring and redeveloping this iconic building and breathe some life back into the city centre and west end of Union Street.”
The property developer will install an escalator to link the refurbished art deco front of house with the new build office development to the rear designed to incorporate stonework, glass and curtain walling.
The building is being developed on a speculative basis and is set to be the largest city centre new build office space under construction.
The Capitol was among the first British cinemas in the Moderne style. Knight’s plans involve the restoration and refurbishment of the retained structures to the front of house including what was the former tea room.