Part of Urban Splash's overhaul of the Grade II*-listed mill complex in Manningham, the curved metal and glass development will provide 24 of the 176 second-phase flats.
The stone buildings, built during the 1870s, were once the largest silk mills in the world and the Morley scheme - which will sit on top of the Velvet Mill block - was inspired by plaited yarns of the material.
David Morley said: 'Working within the constraints of the mill, and with the creativity of Urban Splash, has been incredibly exciting and produced very interesting results.
'Instead of trying to closely match the new with the old, we have used bold new interventions that reflect the ambition of Bradford and express the new life being given to this building.'
Engineer for the scheme, Tim Lucas at Price & Myers, added: 'We used a sophisticated 3D parametric modelling programme, which enabled us to produce a complex, yet apparently simple geometry.'
The two-storey development was given the green light by planners on Friday and it is hoped work can begin on site immediately.