Jose Mourinho's side will face the Spanish league leaders at the Vicente Calderon Stadium in the opening game before playing Diego Simeone's side at Stamford Bridge.
The draw has thrown up an intriguing talking point, with Chelsea reportedly wanting Atletico to pay them in order for on-loan Blues goalkeeper Thibaut Courtois to feature in the tie.
UEFA have released a statement insisting the Belgium international should be free to play in both matches and Chelsea CEO Ron Gourlay confirmed that would be the case, although he did not specify whether a fee would neeed to be agreed first.
"They're all fantastic sides. The important thing to us was to make sure we were in the semi-final," Ron Gourlay told Sky Sports News when asked about the tie itself.
"We need to make sure we are totally prepared for these games. I'm sure Jose will make sure we are but we have some important games before that.
"We have ambitions at this football club and we are evolving all the time. We would like to win back the Premiership and we would like to win the Champions League.
"It will be a fantastic game. It doesn't matter who we play at this stage.
"We will be looking forward to it and for the team that comes through, there is a nice trip to Lisbon as well.
"The key here is that we continue building for the future and we are heading in the right direction.
"We've reached this competition many times in the past 10 years and we are up there competing. We can look forward to the next few weeks and see where we end up."
Mourinho avoided a meeting with former club Real Madrid, who will go up against defending champions Bayern Munich.
That tie sees former Barcelona manager Pep Guardiola, now in charge at Bayern, take on old rivals Real.
Atletico will play Chelsea in the first leg of their tie on 22 April, with the return leg at Stamford Bridge on 30 April.
Real face Bayern at the Bernabeu on 23 April, with the second leg in Germany on 29 April.
The final will take place at the Estadio da Luz in Lisbon on Saturday 24 May.