Munster defeated Northampton in the final pool game on Friday night
Northampton, the only English team in the Heineken Cup quarter-finals, face a reunion with group rivals Munster.
Saints, the lowest-seeded qualifiers, will travel to the two-time champions, who finished above them in Pool One.
The Ospreys, who have reached the last eight for the third straight year, have to travel to 2006 finalists Biarritz.
Defending champions Leinster host Pool Three winners Clermont Auvergne, while three-time winners Toulouse take on Stade Francais in an all-French tie.
The last-eight line-up features four French sides for the first time since 1999, with the potential for two of them to have home semi-finals ahead of the final in Paris on 22 May.
If Leinster overcome the formidable Clermont in Dublin, they face an away semi-final against the winners of the Toulouse-Stade match.
The Ospreys, though, have the carrot of a home semi-final against Munster or Northampton if they can win their quarter-final in France.
Biarritz, struggling in their domestic competition, completed their campaign with a 41-20 win over Glasgow, though the scores were level at 20-20 after an hour.
Toulouse displaced Clermont as the fourth quarter-final host when they won at Sale on Sunday.
The French giants have won six of the seven quarter-finals they have hosted and will start favourites against fellow Top 14 side Stade Francais, who topped their pool despite being beaten by Edinburgh in their final match.
Ospreys made sure of a place in the last eight with an impressive victory over Leicester on Saturday, a result that dumped the two-time champions out of Europe.
The Tigers are appealing, however, after the Ospreys briefly had 16 players on the pitch during the contest.
The Welsh region have reached their third successive quarter-final but will be hoping to reach the last four for the first time.
Of the seven English sides to start the campaign, Northampton are the only ones to have made it through, which represents the worst performance by the country's clubs in the 14 seasons they have taken part in the competition.
Northampton, who defeated Munster to win the 2000 Heineken Cup final, made it through as one of the best runners-up after London Irish suffered a last-gasp draw against Leinster on Saturday.
Saints lost to Munster in the final round of pool games on Friday, although Jim Mallinder's men did win the return match in October.
The third, fourth and fifth best pool runners-up from the Heineken Cup will take part in the last eight of the second-tier Amlin Challenge Cup, and those places were confirmed on Sunday.
Cardiff Blues made sure of their place with a comfortable six-try victory at Harlequins, and they will travel to Newcastle - who won their Challenge Cup pool - in the quarter-finals.
Wins for Gloucester - who travel to Wasps - and the Scarlets, who travel to face Jonny Wilkinson's Toulon - put them in the hat, with Ulster and Sale missing out.
The other quarter-final sees Irish province Connacht, who won their pool, host French side Bourgoin, who won at Leeds to book their place at the expense of the English club.
Toulon's bonus-point win over Castres saw Saracens miss out.
Heineken Cup quarter finals:
Munster v Northampton (to be played on 10 April, 1730 BST)
Biarritz v Ospreys (10 April, 1500 BST)
Toulouse v Stade Francais (11 April, 1630 BST)
Leinster v Clermont Auvergne (9 April, 2000 BST)
Challenge Cup quarter-finals:
Connacht v Bourgoin
Toulon v Scarlets
Wasps v Gloucester
Newcastle v Cardiff Blues
Ties to be played on the weekend of 9-11 April
Heineken Cup semi-finals:
Toulouse/Stade Francais v Leinster/Clermont Auvergne
Biarritz/Ospreys v Munster/Northampton
Ties to be played on 1-2 May