Madrid and Bayern have combined to win 14 European Cup or Champions League titles. They have also been runner-up eight times, yet never have met in the final.
Five-time winner Bayern is looking to become the first team in 24 years to repeat as Europe's top club.
''We acknowledge that Bayern Munich, since the beginning of the season, the performance has been amazing,'' Real Madrid director Emilio Butragueno said. ''But we are Real Madrid and when we compete, we compete to win.''
Atletico will host the first leg on April 22 against Chelsea, which it routed 4-1 in the UEFA Super Cup two years ago. Real will be home for Bayern the next day.
The return matches are April 29 and 30. The final is May 24 in Lisbon, Portugal.
''We are the teams who are playing the most attractive football right now,'' former Bayern and Real Madrid great Paul Breitner said.
Madrid-Bayern is a repeat of the semifinals two years ago decided by a penalty-kick shootout at the Santiago Bernabeu Stadium after each team won 2-1 at home. Then, Cristiano Ronaldo was among three Madrid players who failed to score from the spot.
The semifinal lineup includes three coaches who each have two Champions League titles with other clubs: Bayern's Pep Guardiola won with Barcelona in 2009 and '11; Madrid's Carlo Ancelotti with Milan in 2003 and '07; Chelsea's Jose Mourinho with FC Porto in 2004 and Inter Milan in '10.
Mourinho could become the first to coach three clubs to the European title. Guardiola and Ancelotti aim to become the fifth coach to guide two different clubs to the title. The odd man out, Atletico coach Diego Simeone, won a Europa League title with the club in 2012.
Ancelotti also played for AC Milan when it was the last back-to-back champion, winning the European Cup in 1989 and '90. The Italian coach is seeking to take Real Madrid to its first final in 12 years. Under Mourinho, it lost in the semifinals for the past three seasons.
''I'm confident we can do what is needed to win,'' Ancelotti said. ''Guardiola is one of the best coaches in the world and the series against Bayern will be difficult for both teams.''