South Africa and Fiji became the first sides to qualify for the Rugby Sevens tournament at the Rio 2016 Olympics.
Leading the World Rugby Sevens Series, the South Africans booked a quarter-final berth in the Glasgow Sevens at Scotstoun and with it a place in Brazil next year before Fiji followed suit.
The two teams will, coincidentally, meet each other in the last eight.
The South Africans began their day with a 19-12 victory over Samoa, then assured themselves of a place in the last eight on Sunday with a 22-5 victory over Kenya. They were given a fright by the Kenyans, though, who led 5-0 at half-time before succumbing to two tries from Seabelo Senatla after Kyle Brown had levelled matters.
Fiji, who have won three of the seven tournaments so far, made a clean sweep of their pool, beating Wales 40-17, Portugal 49-12 and hosts Scotland 45-5.
"It feels a little bit emotional," Fiji coach Ben Ryan said. "We've put in so much work to get to this stage, and I know everyone on the island will be delighted with this. It's really a fantastic day for Fiji."
Defending series champions and Glasgow champions New Zealand put a slight dent in South Africa's celebrations by beating them 24-19 in their pool match
New Zealand can also qualify for Rio if they reach the semi-finals on Sunday, though they will have to beat the hosts.
In the other quarter-finals, Canada take on England while Australia will face the United States.
Sevens makes its Olympic debut next summer, though rugby has featured in the summer games previously, with the last 15-a-side event staged during the 1924 Games in Paris. It follows a successful Sevens event during last year's Commonwealth Games in Glasgow, where South Africa took gold.