The Los Blancos were eliminated by the English side last season en route to Thomas Tuchel’s side lifting their second Champions League title.
Chelsea after advancing from the group stage beat Lille with a 4-1 aggregate to secure a quarterfinal berth while Madrid also came from a 1-0 deficit in the first leg to eliminate Paris Saint-German.
Manchester City will also battle it out with Atletico Madrid in the last eight of the competition in another England-Spain battle.
The Spanish side will welcome City to the Wanda Metropolitano in the first-leg before travelling to the Etihad for the reverse fixture.
In other fixtures, six-time winners will go head-to-head with Portuguese side, Benfica while Bayern Munich and Villarreal wrap up the quarterfinal draw.
Benfica progressed to the last 8 of the competition following their 1-0 win over Ajax in Amsterdam with Villarreal also beating Juventus for a place in the next phase of the competition.
The first legs of the quarterfinal ties will be played on 5/6 April with the second legs on 12/13 April.