The derelict Westmoreland House on Stokes Croft will be demolished and the adjoining Carriageworks renovated for business units and 118 new homes.
Bristol City Council deferred making a decision on the proposal in April after protests against the lack of social housing in the design.
The scheme was approved after changes to the original plans were made.
These included the removal of gates and increasing the number of affordable properties in the development.
Lori Streich, from the Carriageworks Action Group, described the planning approval as "incredibly good news", and said it is "a very significant step to achieving an end to the dereliction of that site".
Comer Homes currently owns the buildings, but is to sell to Fifth Capital now planning approval has been granted.
The two buildings have been vacant for more than 25 years and Bristol City Council hopes the scheme will help regenerate Stokes Croft.
The area is regarded as the "spiritual home" of the street artist Banksy as his famed mural The Mild Mild West resides near Jamaica Street Junction.
Plans for a £20m revamp of an area of Bristol considered one of the city's biggest eyesores have been approved.