Tigers finished second to Perpignan in Pool 5 after scoring nine tries in a 62-15 win over Benetton Treviso at Welford Road on Saturday.
The result guaranteed Tigers’ passage into the last eight as seventh seeds and the best of the runners-up.
And London Wasps’ 21-16 win over Toulouse later on Sunday afternoon meant it was Pool 2 winners Leinster who qualified as the second seeds.
It sets up a repeat of the 2009 Heineken Cup Final at Murrayfield, when the pair last clashed in Europe.
The Heineken Cup quarter-finals are scheduled for the weekend of April 9. Kick-off dates and times will be confirmed with tournament organisers ERC. Ticket details will be confirmed once the fixture date has been set. Keep your eye on the Tigers website for details.
Quarter-final line-up: Northampton Saints v Ulster, Leinster v Leicester Tigers, Perpignan v Toulon, Biarritz v Toulouse
The semi-final draw was also made on Sunday afternoon and the winner of Tigers’ clash with Leinster will enjoy home country advantage against the winners of the tie between Biarritz and Toulouse. The other semi-final will see Saints or Ulster given home country advantage against either Perpignan or Toulon.