The Serie A giants stood firm in the face of unrelenting Barcelona pressure to hold on to their 3-0 first led advantage and eliminate Luis Enrique's side.
Monaco, the Ligue 1 leaders, scored twice inside the opening 20 minutes to all but end Borussia Dortmund's fight back, with Marco Reus scoring shortly after half-time only for Valere Germain to settle the tie in the 81st minute.
The Madrid pair sealed their routes through to the last four on Tuesday, with Real bettering Bayern Munich after extra time in a game littered with controversy over a number of the goals scored.
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Cristiano Ronaldo scored a hat-trick, scoring his 100th Champions League goal in the process, though there were question marks over if the Portuguese was offside in two of them.
Real become the first team to reach the semi-finals in seven consecutive seasons and are aiming to become the first team to retain the trophy.
The last time Atletico, Juventus and Monaco reached the semi-final stage they also went on to reach the final and all lost, Monaco to Jose Mourinho's Porto in 2003-04, Juventus to Barcelona in 2014-15 and Atletico to Real last season.
The semi-final first legs will take place on Tuesday, May 2 and Wednesday, May 3, with the second legs the following week.
The draw for the Champions League semi-finals will take place on Friday, April 21 at 12pm at Uefa's headquarters in Nyon.