Angola, Dominican Republic, Greece, Jordan, Korea, Lithuania, Macedonia, New Zealand, Nigeria, Puerto Rico, Russia and Venezuela are going for three available slots in the men's draw.
And Team GB coach Chris Finch will not learn of his opponents until just three weeks before the Games, with world number four Greece and number five Lithuania potentially lurking.
Great Britain, ranked 43rd in the world, will then face matches against Brazil, 2008 Olympic silver medallists Spain, Australia, who Great Britain pushed to overtime at last year's test event, and China.
Meanwhile, Tom Maher's British women's team will play their first-ever Olympic match against world number two side Australia on July 28, they will also face group games against two qualifiers, Brazil and Russia.
Red-hot medal favourites the USA, who will bring a powerful team of NBA stars to defend their men's title, will tip-off their campaign against France.
"For every major championship, the draw and subsequently the unveiling of the full competition schedule make for a major milestone," said Fiba general secretary Patrick Baumann.
"Players begin picturing themselves on the court and thinking about match-ups and fans start imagining the atmosphere.
"The 2008 men's final between the USA and Spain was one of the greatest Olympic moments.
"It showed the huge strides international basketball had made in becoming more and more competitive. I expect this year's Olympic basketball tournaments will be a great and memorable spectacle for all."