The Pacific islanders were seeded first in the draw for the Aug 9-11 tournament in Brazil after landing a second successive World Series crown this year.
Third seeds New Zealand, champions 12 times in 17 editions of the World Series, face a united Britain side composed of players from England, Scotland and Wales as well as Kenya and Japan.
Women's top seeds Australia, who won their first World Series title in May, face United States, Fiji and Colombia in their pool at the Aug 6-8 competition, which will mark the return of rugby to the Olympics for the first time since 1924.
The top two teams from each pool as well as the two best third-placed sides progress to the quarter-finals in both tournaments.
Draws (numbers indicate seeding):
Men
Pool A: 1-Fiji, 6-United States, 7-Argentina, 12-Brazil
Pool B: 2-South Africa, 5-Australia, 8-France, 11-Spain
Pool C: 3-New Zealand, 4-Britain, 9-Kenya, 10-Japan
Women
Pool A: 1-Australia, 6-United States, 7-Fiji, 12-Colombia
Pool B: 2-New Zealand, 5-France, 8-Spain, 11-Kenya
Pool C: 3-Canada, 4-Britain, 9-Brazil, 10-Japan
(Reporting by Nick Mulvenney and Andrew Downie; editing by Greg Stutchbury)
