Friday's decision ends almost two years of wrangles about the project with local planners and has delighted American art dealer Kenny Schachter, who is backing the 900m 2development in Hoxton Square.
Set to open in early 2008, the building looks likely to be completed before Hadid's other major London commission - the much-troubled Architecture Foundation project, which is now being worked on with Allies and Morrison (AJ 26/01/2006).
The Hoxton Square project, which will house a ground-floor gallery, offices and apartments, seemed to have come off the rails last summer when Hackney Council sent the architect back to the drawing board over 'land-use issues'.
However, Schachter said it is now full-steam-ahead for the scheme, which will replace an existing 1980s building on the east side of the square.
He said: 'I am thrilled that this long, convoluted process has culminated in approval so we can finally get moving on a project that began in earnest two years ago.
'With Hadid's Guggenheim Museum opening and [a retrospective of her work] fast approaching-. the timing couldn't have been more propitious.'
Work on site is due to start in the autumn.