Real Madrid will play defending champion Bayern Munich in the Champions League semifinals, and Atletico Madrid will face Chelsea.
Madrid and Bayern have combined to win 14 European Cup or Champions League titles. They have also been runner-up a further eight times, yet never met in the final.
Five-time winner Bayern is seeking to become the first team in 24 years to repeat as Europe's top club.
Atletico will host the first leg against Chelsea, which it routed 4-1 in the UEFA Super Cup two years ago.
The first legs will be played April 22 and 23, with the return matches on April 29 and 30.
The final is scheduled for May 24 at the Stadium of Light in Lisbon.