Their success emulated that of the Spain men's team, who stunned Samoa in Monaco last week to clinch the 12th and final spot in Rio.
"It's amazing," Spain playmaker Patricia Garcia said.
"I'm really, really happy for the team – we are the happiest girls in the world at the moment because now we get to go to the biggest sporting stage of them all in Rio. It's an incredible feeling.
"Our men qualifying last week has been the inspiration for us all week. We took their example with the teamwork we showed. I am pretty emotional but with smiles, not tears."
Rugby union returns to the Olympic programme for the first time in 92 years in August when men and women compete for gold in the shorter version of the game at the Deodoro Stadium.
(Reporting by Nick Mulvenney; Editing by Greg Stutchbury)
