Planning paves the way for Sir Robert McAlpine and US construction partner B L Harbert to start construction work next spring on the 500,000 sq ft glass cube building.
The 12-storey blast-proof cube sits on top of a colonnade, surrounded by a park and lake that some have dubbed “the moat.”
Wandsworth council’s planning chairman, Nick Cuff, said: “The embassy’s move is already acting as a magnet for new investment in this part of London which has started to change on an enormous scale.
“Once it opens its doors the complex will attract more than 1,000 visitors every day, boosting the local economy and bringing new life to this stretch of the South Bank.”