It will also be the third time the two teams have met on the old Lansdowne Road site. This season the Tigers reached 100 games in the Heineken Cup and they kicked-off their European adventures with a 27-10 triumph over Leinster at Lansdowne Road in a game in which current coach Richard Cockerill was the visitors' hooker.
Leinster, who beat the Tigers 19-16 at Murrayfield two years ago to take the title for the first time, have already played two matches at the new home of Irish rugby this season and are unbeaten at the re-built venue.
They beat Munster in a Magners League game and ASM Clermont Auvergne in one of their Heineken Cup Pool matches before Christmas at the 51,700 all-seater stadium.
"In our two fixtures at the Aviva Stadium to date we have enjoyed two outstanding spectacles with the team having been inspired to victory by close to 100,000 supporters," said Leinster chief executive Mick Dawson.
"To reach the knock-out stages, and achieve a home quarter final draw in the process, is an impressive achievement and due reward, not only for the team, but also for our loyal supporters," said Leinster chief executive Mick Dawson.
"The fans have followed the team across Europe at great expense and also established their own reputation as a significant element in the Leinster quest to regain the Heineken Cup. More than 1,000 supporters made the trip to Paris last weekend and gave wonderful vocal support throughout the game."
Full ticket details for the Heineken Cup quarter final will be available in the coming days once the kick-off time and date have been confirmed by ERC.
The quarter-final will be the 11th time to the two teams have clashed in the Heineken Cup and their sixth meeting in Dublin.