The 2015 Rugby World Cup winner will come from the southern hemisphere, after all four quarterfinals ended in defeat for northern nations. Australia will now face Argentina, while South Africa will take on New Zealand.
Australia was the final team to clinch a place in the quarterfinals with a narrow victory over Scotland at London's Twickenham stadium on Sunday.
The Scots had been within a whisker of a shock victory over the Wallabies, after Scotland's Mark Bennett intercepted an Aussie pass to charge in a try in the 74th minute.
After Scottish captain Greig Laidlaw converted to put his side 34-32 up, a place in the quarterfinals looked tantalizingly close for the Scots.
However, the South African referee awarded Australia a controversial penalty for offside, which was successfully kicked by Australia's Bernard Foley to break Scottish hearts. The penalty decision was considered harsh, with Scottish fans - including police in the town of Falkirk - expressing their frustration.
In the earlier game, Argentina - the weakest of the southern hemisphere's big four teams - had far less trouble to overcome Ireland, who were put to the sword 43-20.
Pumas' flyhalf Nicolas Sanchez played an almost flawless game to help engineer the shock win - not the first surprise win of the tournament.
First day of pain for North
On Saturday, France were thrashed 62-13 by a ruthless New Zealand team that is a favorite to win the title. Like Scotland, Wales were only defeated by a narrow margin when South Africa's Springboks used a last-minute scrum-move to see off their opponents 23-19. New Zealand coach Steve Hansen, a former Wales boss, said the southern hemisphere teams all benefited from playing each other regularly.
"If you look at the three teams they are different... So, the competition creates a rugby player that can be multi-functional."
"The environment and weather down with us helps too. When you contrast that with the northern hemisphere, when you can be playing in snow and rain and freezing cold. That is not conducive to playing running rugby," he said.
It's the first time that there will have been two all-southern hemisphere semifinals, although the team that wins the tournament's Webb Ellis Cup almost always comes from the southern hemisphere.
The only northern hemisphere side to ever break the southern grip on the tournament has been England, who won the tournament in the 2003 final in Sydney. This time around, though, fortune did not favor the English, who were the first-ever tournament hosts to exit the competition before the knockout stage.
rc/cmk (AP, AFP, dpa)