The French league leaders Monaco will take on the Italian champions Juventus in the other semi-final.
The first legs will be played on 2 and 3 May, with the return legs the following week.
Real are aiming to win European club football’s most prestigious competition for a 12th time. They beat the German champions Bayern Munich 6-3 on aggregate to reach the last four.
Atletico advanced following a 2-1 aggregate win over the English champions Leicester City.
Juventus arguably registered the most impressive result. They overwhelmed Barcelona 3-0 in Turin and then held the Catalans 0-0 at the Camp Nou in the second leg while Monaco defeated Borussia Dortmund 6-3 over the two legs.
In the second tier Europa League, Lyon will play Ajax while Manchester United face Celta Vigo. The winner of the competition will gain a place in the group stages of the Champions League.