French club Marseille will play FC Salzburg, the club backed by soft drinks giant Red Bull, in the other semi-final.
Arsene Wenger's Arsenal will play the first leg at the Emirates Stadium against Atletico, led by French striker Antoine Griezmann, who are favourites to win the competition for the third time.
The first legs will take place on April 26 with the second on May 3.
Arsenal reached the last four after surviving a scare against CSKA Moscow in Thursday's quarter-final second leg in the Russian capital.
Danny Welbeck and Aaron Ramsey both scored late in the game for Arsenal to calm nerves after CSKA had raced into a 2-0 lead on the night. The London side won 6-3 on aggregate.
Atletico lost 1-0 to Sporting in Lisbon on Thursday but advanced 2-1 on aggregate.
Marseille overcame a first-leg deficit to beat German side Leipzig 5-3 over two legs in their quarter-final, while 1994 finalists Salzburg produced the shock result of the night by defeating Italian side Lazio 4-1 at home to win 6-5 on aggregate.
Salzburg have already beaten Marseille once in the competition this season, a 1-0 victory in Austria. The teams also drew 0-0 at the Velodrome.
"But this time it's the semi-final so it'll be different," Marseille director Andoni Zubizarreta told beIN Sports.