Development managers Mitsui Fudosan and Stanhope picked Multiplex to start the next phase after its rival Mace completed the first phase of the vast scheme.
Multiplex will act as construction manager on the £200m-plus job to deliver 345 flats in two blocks.
Multiplex secured the project following a break-through £120m deal with Stanhope last summer to redevelop the IBM building on London’s South Bank.
Enabling works and site preparation will start at the Television Centre scheme in the autumn underlining confidence in the White City homes market.
Multiplex will build out two separate plots designed by practices dRMM and AHMM. A total of 511 homes will eventually be built over four separate plots in the second phase.
Main construction is due to commence in 2024.
Jonathan Trout, Property & Commercial Director at Stanhope, said: “We are delighted to be working with Multiplex for the development of 345 new homes on this iconic site which we expect to complete by 2026.
“The start of phase 2 demonstrates the commitment of Stanhope and Mitsui Fudosan to the delivery of much needed new housing, including affordable, in Hammersmith & Fulham and our long-term commitment to the area.”