Designed by architects Pilbrow and Partners, the proposals at Centre House include two landmark 22-storey and 32-storey buildings and a new curved crescent of housing.
Around a third of the homes will be affordable homes, allocated to staff at Imperial and other key workers.
The gateway project forms part of the wider 10 acre White City Living major regeneration scheme that will eventually provide more than 2,300 homes.
The planning consent follows more than two years of consultation and engagement with Hammersmith & Fulham Council and represents the next phase of the regeneration of White City.
Works will start on site in late autumn, with construction due to commence in 2021 and the first homes expected to be completed by 2024.
Sean Ellis, Chairman of St James Group, said: “Centre House is the final piece of the jigsaw in the White City masterplan and is pivotal in connecting the major regeneration projects that surround it.
“We have worked closely with Imperial College London and Hammersmith & Fulham Council to create a high-quality new vision for the site, providing a significant number of key worker and private sale homes.”