Fellow Irish province Munster, who won the title in 2006 and 2008, will be third up on Saturday afternoon when they host the 2000 champions Northampton Saints in a re-match of their recent pool match in Limerick.
The first of the two quarter-finals on French soil will launch the Saturday sequence of matches when Biarritz Olympique entertain the Ospreys.
Pool 2 winners Biarritz will be taking their fixture across the border into Spain, to play at the 32,000-capacity Estadio Anoeta in San Sebastian. It will be the fourth knock-out match Biarritz have played at the venue and their sixth game overall.
As well as beating Munster and Sale Sharks in the last-eight in Spain, they also defeated Bath there in the semi-finals in 2006.
Their only Heineken Cup defeat in San Sebastian came in 2007 when Northampton Saints pipped them 7-6 in the quarter-finals.
Three-time champions Toulouse, who meet Stade Francais in an all-French affair on Sunday, April 11, have also agreed to switch their game to a bigger stadium. They have already beaten Sale Sharks and Cardiff Blues at Toulouse's 37,000-capacity Stade Municipal this season.
2009/10 HEINEKEN CUP QUARTER-FINALS:
All kick-off times local time -
FRIDAY, APRIL 9
LEINSTER v Clermont Auvergne, 8pm (Sky Sports/Canal+Sport)
SATURDAY, APRIL 10
Biarritz Olympique v Ospreys, 4pm (France 2/Sky Sports)
MUNSTER v Northampton Saints, 5.30pm (Sky Sports/Sport +)
SUNDAY, APRIL 11
Toulouse v Stade Francais, 5.30pm (France 2/Sky Sports)