Leicester's reward for their stunning victory over holders Munster in Limerick on Saturday is a clash against French Championship leaders Stade Francais, the club they beat to be crowned 2001 European champions
Wasps, the 2004 Heineken Cup winners, will entertain Brian O'Driscoll's Leinster for the first time in tournament history, while Munster face a difficult away tie against Welsh challengers Llanelli Scarlets.
Northampton, who qualified as one of two best runners-up from six pools, face a reunion with top seeds Biarritz, probably in San Sebastian.
The Saints lost 17-8 at home to Biarritz on Sunday, and will travel as rank outsiders against a side contesting their fifth successive quarter-final.
Heineken Cup quarter-final line up:
Biarritz v Northampton, Llanelli Scarlets v Munster, Wasps v Leinster, Leicester v Stade Francais.
Ties to be played on weekend of March 30-April 1.