Argentina were unbeaten in the South American qualifying tournament, played in the northern Argentine city of Santa Fe.
Only Chile, who with Uruguay earned a spot in a final men's qualifying tournament, troubled them in their six matches before the hosts ran out 17-10 winners on Friday.
"We came here to achieve this and we're very happy," Argentina's Franco Sabato, who scored two tries against Uruguay, was quoted as saying by the Argentine Rugby Union.
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"We knew Uruguay would give us a tough match but we had faith in our game."
Colombia's women won all seven of their matches to book their place at the Rio Games, where rugby is making an Olympic comeback after 92 years.
Argentina and Venezuela qualified for the final women's qualifying tournament. Brazil's men's and women's team qualified as hosts.
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