Paris St Germain and Barcelona were paired together having met in the group stage, with the French side winning in Paris and the Catalans coming out on top in Spain.
Porto will face 2013 champions Bayern Munich and Juventus take on Monaco in the other ties.
The fixtures will be played on April 14/15 and April 21/22, with PSG, Atletico, Porto and Juventus playing the first legs at home.
Real won last year's final 4-1 after extra time against their local rivals, but Atletico's superb recent record against their more illustrious neighbours will give them huge cause for optimism.
The teams have met six times in all competitions this season with Real Madrid yet to register a win, while last year's final was Real's only victory in the last eight derbies.
Carlo Ancelotti's side have drawn three and lost four of those eight games while the last Madrid derby ended in a 4-0 win for Atletico, their biggest victory against their rivals since 1987.
Real's recent form has also been less than impressive having ceded the advantage in La Liga to Barcelona and suffered a surprise wobble in the last 16 against Schalke 04 when they slumped to a 4-3 defeat at the Bernabeu to squeeze through 5-4 on aggregate.
"Atletico are a very competitive team," Real director Emilio Butragueno told Canal Plus.
"But we are Real Madrid, we are defending the title and we will try to perform well enough to get through the tie."
Porto's clash with Bayern is a repeat of the 1987 final when the Portuguese side came out on top 2-1 in Vienna.
Bayern will start as overwhelming favourites, however, against an inexperienced Porto side, with the Germans offering a potent reminder of their pedigree in a devastating 7-0 drubbing of Shakhtar Donetsk in the last 16.
"There are certainly more uncomfortable opponents," Bayern captain Philipp Lahm said.
"But they (Porto) have showed their class. We will try to get in our away match an even better result than in the last 16. We are Bayern and we know what we have achieved in the last few years."
(Writing by Toby Davis in London; editing by Ed Osmond)
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