The 30 million Swiss francs (£20 million/$31 million) project, which seen from above is shaped like a hand and incorporates structural elements strongly resembling a basketball net, should be finished during the winter of 2012-2013.
FIBA President Yvan Mainini told assembled guests, including International Olympic Committee (IOC) President Jacques Rogge: "A birth like this is something very important.
"FIBA was created in 1932 in Geneva and today is like a re-birth as we break ground here to give the federation the dynamism it will need in coming years.
"We look forward to this project being completed so that we can welcome you all here again in two years' time."
Rogge said: "Basketball is a universal sport.
"It requires very little infrastructure and therefore is ideal to be played at school level.
"It is a sport where there is no violence, that carries values and that is very appealing.
"I would like to congratulate FIBA for this great initiative.
"This building will allow FIBA to do an even better job of fulfilling its mission regarding basketball and the development of the sport."
As well as the administrative offices of FIBA, the building will house the newly-set up International Basketball Foundation (IBF) and the FIBA Hall of Fame.
During the ceremony, a capsule was filled with basketball objects and memorabilia including a signed ball, a game jersey and a book on the history of FIBA that will be cemented into the building's foundations.