The 50m-tall office building designed by Make Architects will be cloaked in LED cladding to display advertising and public art.
The 50,000 sq ft Chiswick Roundabout scheme also includes a retail showroom at ground level and a rooftop temperate garden and public viewing gallery.
An earlier design was refused permission by Hounslow’s Planning Committee in March 2010 because of fears the advertising space would distract drivers on the motorway.
Since then, a public inquiry concluded that there was no adverse impact on highway safety.
The resolution to grant consent for the project was passed despite the recommendation of officers for refusal.
Kim Gottlieb, managing director at London & Bath Estates, said: “For one of the world’s greatest cities, a truly iconic building to mark the entrance along its primary transport route is long overdue.
“The Octopus will create a point of focus and attract interest in this part of London, creating jobs and providing an economic boost at a time when this is sorely needed.”