Chelsea will play Atletico Madrid for a place in the Champions League final, while the other semi-final pits holders Bayern Munich. The first will take place on April 22/23 and the return the following week.
The draw sets up an intriguing situation with goalkeeper Thibaut Courtois - the 21-year-old goalkeeper on loan with Atletico from Chelsea. It was reported that Chelsea would allow the Spanish side to play the Belgian in both legs of the semi, provided they paid a fee of around 3million euros for each game.
However, UEFA moved to clarify that it expects the Belgium international to be free to face the Blues in both legs. A statement from European football's governing body read: "The integrity of sporting competition is a fundamental principle for UEFA.
"Both the UEFA Champions League and the UEFA disciplinary regulations contain clear provisions which strictly forbid any club to exert, or attempt to exert, any influence whatsoever over the players that another club may (or may not) field in a match.
"It follows that any provision in a private contract between clubs which might function in such a way as to influence who a club fields in a match is null, void and unenforceable so far as UEFA is concerned. Furthermore, any attempt to enforce such a provision would be a clear violation of both the UEFA Champions League and the UEFA disciplinary regulations and would therefore be sanctioned accordingly."
Real's pairing against Bayern brings together two clubs who have won the competition 14 times between them. Five-times winners Bayern, quarter-final conquerors of Manchester United, are the defending champions.
Real, who booked their place in the last four with a win over Borussia Dortmund, have won European club football's top prize nine times - but not since 2002.
Chelsea will play the first leg in the Spanish capital as they seek to book a place in this season's final in Lisbon. On Courtois, chief executive Ron Gourlay said: "The loan was arranged at the start of the season. He could play against Chelsea - that was never in doubt.
"Regarding the (UEFA) statement that came out, we'll evaluate it over the next 24 to 48 hours. As far as we're concerned we complied with loan rules. He can play against Chelsea - if selected."
On the draw itself, Gourlay continued on Sky Sports News: "They're all fantastic sides. The important thing to us was to make sure we were in the semi-final. We need to make sure we are totally prepared for these games. I'm sure Jose will make sure we are but we have some important games before that.
"If someone had said at the start of the season we'd be in the Champions League semi-finals and the Premier League (title) shake-up I'd have taken it. This is what we work for all season. We have ambition at the club, it's evolving all the time. We'd like to win back the Premier League and add another Champions League win (to the 2012 success).
"The key is to keep building for the future and we're definitely heading in the right direction. We're in a good position and everyone's done fantastically well. We can look forward to the next few weeks."
Meanwhile, Real Madrid coach Carlo Ancelotti was looking forward to his team's clash against the defending champions. Ancelotti, whose side lost their quarter-final second leg 2-0 to Dortmund on Tuesday but went through 3-2 on aggregate, told a press conference: "Yes, we were poor against Dortmund but it doesn't matter because we made it through.
"If we want to win the Champions League we then have to beat everyone, including Bayern. The games will be very difficult, but it's not easy for anyone to play Real Madrid either."
The match will see former Barcelona coach Pep Guardiola return to Spain and Ancelotti added: "He is one of the best coaches in the world. They have a great team."