The scheme, which forms part of Allies and Morrison's Bankside 123 masterplan, will be paid for by developer Land Securities.
The designs for the project, which would be Hadid's first in London, have evolved heavily since the Pritzker Prize-winner won the competition for the building at the beginning of 2005, seeing off the likes of young guns AOC.
Hadid has also work closely with Allies and Morrison on the scheme, which is set to cost almost double the original budget ( Allies and Morrison to oversee Zaha at Architecture Foundation).
The backers of the building - which will include three different-sized galleries and an administration area - hope that it will become part of Southwark's 'cultural quarter', which includes the Globe Theatre and Tate Modern.
Hadid said: 'I am absolutely delighted that the designs for the new Architecture Foundation headquarters have secured planning permission.
'The centre will be my first public building in London, and is therefore an especially important project for my practice,' she added.
It is planned that the building should complete in 2008.