The partnership submitted a planning application last month to deliver two buildings totalling 245 flats to the south of the railway station.
The client delivery team also includes: engineering consultant WSP; architect Ryder and project manager Faithful and Gould.
The historic Tower Works site will deliver ground floor commercial uses as well as extensive new areas of public realm to enable a pedestrian route through from the city centre to the Holbeck Urban Village neighbourhood.
Mark Gibson, managing director for the Scotland and Northern Region at Sir Robert McAlpine, said: “We are thrilled to be appointed as lead contractor on Tower Works for Richardson.
“We are already involved in the regeneration of the South Bank with the adjacent Mustard Wharf development, and this scheme is an exciting addition.”
Ben Holmes, real estate director for Richardson, said: “The early appointment of Sir Robert McAlpine as main contractor demonstrates our clear intention to make an immediate start on site following the determination of planning.”
Gareth Callen, partner at Ryder Architecture, added: “Tower Works is a unique setting – our concept designs respect the context and environment of the listed towers by combining the classical proportions of the towers with the rigour of Leeds’ industrial heritage.”