The developers also plan to build 290 flats in several buildings of up to 15 storeys, a new Waitrose, several shops and a cinema for the area.
But the scheme has run into stiff local opposition from residents, who complain the apartment blocks will blight a stretch of the River Thames.
The King Street Regeneration project was put together by the developers following a competition by the borough council designed to attract ambitious proposals for the area.
But the scheme could now face an appeal from local opposition groups who have been vocal in their attack on the plans.
Councillor Mark Loveday, the council’s cabinet member for strategy, said: “This is excellent news for Hammersmith and it is good news that the plans, reduced by KSD in the summer, have now got the go ahead.
“It is good news for businesses in and around King Street that will get an economic shot in the arm when the project is complete.
“It is good news for people who are hoping to get onto the property ladder. And it is good news for taxpayers who will not need to find £18m to refurbish the ugly town hall extension.”