Eleven-time European champions Real, who eliminated Bayern Munich in the quarterfinals, could become the first club in the Champions League era to win the competition in successive seasons.
The Madrid clubs have met in the Champions League final in two of the last three years, with Real coming out on top on both occasions.
Atletico had also reached the final in 1974, when they lost to Bayern, but have yet to win the competition.
Atletico director Clemente Villaverde said the club were not daunted after being drawn against Real Madrid in the Champions League semifinals, while Real director of institutional relations Emilio Butragueno said past meetings will have no bearing on the clash.
The other tie sees Ligue 1 leaders Monaco take on Italian champions Juventus.