The Blues got the upper hand when the sides clashed in the 2009 final at Murrayfield, with Jonathan Sexton's 70th-minute penalty steering them to a famous 19-16 win.
Leicester, who currently top the Aviva Premiership, defeated Leinster in quarter-final ties in 2002 and 2005.
For their first quarter-final since the 1998/99 season, Ulster will relish the task of going to Northampton to try to end Saints' unbeaten run in this season's competition.
The reward for the winners of the Leinster v Leicester and Northampton v Ulster games is 'home country' advantage in the semi-finals. The draw for the semi-finals was made this evening - click here for full details.
Northampton's squad includes ex-Ulster back rower Roger Wilson, whose side secured the number one seeding after London Wasps' dramatic round 6 win over defending champions Toulouse.
The French giants are away to Biarritz Olympique in the last-eight, in what is a repeat of last season's final. Munster's conquerors, Toulon, will travel to Perpignan in the second all-French tie.
The quarter-final matches will be played over the weekend of April 8 to 10.
Meanwhile, Munster are one of the three Heineken Cup pool runners-up to qualify for the Amlin Challenge Cup quarter-finals.
Tony McGahan's men are away to French side Brive in the knockout stages of European club rugby's second tier tournament. If they win that match, they will have a home semi-final against either Harlequins or London Wasps.
Brive lost to Leinster home and away last season and are currently third-from-bottom in the Top 14 table. However, they did manage to go unbeaten during the pool stages of the Amlin Challenge Cup, claiming a notable double over Sale Sharks.
The Amlin Challenge Cup quarter-finals will take place over the weekend of April 8 to 10.
2010/11 HEINEKEN CUP QUARTER-FINALS:
Northampton Saints v ULSTER
LEINSTER v Leicester Tigers
Perpignan v Toulon
Biarritz Olympique v Toulouse
2010/11 AMLIN CHALLENGE CUP QUARTER-FINALS:
Stade Francais v Montpellier
Brive v MUNSTER
La Rochelle v Clermont Auvergne
Harlequins v London Wasps
- Ties to be played over the weekend of April 8/9/10