Sources close to Berkeley said Laing O'Rourke would be formally appointed in the next few weeks.
The site of the scheme is being excavated, and is subject to an archaeological dig. Laing O'Rourke is due build the Rolfe Judd-designed scheme in August.
The project, in Tabard Square, Borough, received planning permission last October and includes 30% affordable housing. Of the 521 units planned, 40 will be for key workers and 122 low cost.
The scheme is made up of three buildings, each of six to eight storeys, and a 21-storey tower. The project team includes QS KHK, structural engineer FaberMaunsell, and services engineer Ecosphere Services.
Laing O'Rourke is also expected to pick up a £23m mixed-use scheme in Hemel Hempstead for housebuilder Crest Nicholson.
It edged out rival Balfour Beatty to clinch the deal. Contractors HBG, Sir Robert McAlpine and Norwest Holst also bid for the scheme in March.
The development, designed by architect Bernard Engle, will include a retail centre and a 100-bedroom hotel on the former headquarters of oil company BP. Work is due to start in the summer and will be completed by 2005.
The Fitzroy Robinson-designed building is the first phase of the Harbourside scheme, and is pre-let to banking group HBOS.
Contractors including Kier, Carillion and Sir Robert McAlpine are expected to tender for the project. One source said winning the first phase could lead to further work, worth up to £35m, on future phases of the scheme.