Liverpool will play Villarreal in the Europa League semi-finals.
The Reds' reward for Thursday's dramatic victory over Borussia Dortmund is a trip to Spain for the first leg on 28 April, with the return at Anfield on 5 May.
In the other semi-final, Spanish side Sevilla, who are looking to win the competition for the third successive year, face Ukraine's Shakhtar Donetsk.
The final takes place in Basel, Switzerland, on 18 May.
|What happens if Manchester City and Liverpool win the Champions League and Europa League?|
|Winners of the Champions League and Europa League are guaranteed to qualify for next season's Champions League.|
|A maximum of five clubs per country are allowed to compete in the Champions League.|
|So should Manchester City AND Liverpool both win their respective titles but finish outside the top four, only the Premier League's top three would qualify for the Champions League, alongside the two European competition winners.|
|A European trophy for both Manchester City AND Liverpool would mean Manchester United or West Ham missing out on the Champions League even if they finish fourth in the Premier League.|
|England would not gain an extra spot in the Champions League if either Manchester City or Liverpool win their respective competitions and finish in the top four.|
Liverpool staged one of the most sensational comebacks Anfield has seen to overcome their German opponents in Thursday's quarter-final second leg.
They were twice left needing three goals to go through, with Dejan Lovren's injury-time header from James Milner's cross sealing a 5-4 aggregate victory on a night packed with drama and emotion.
|Re-cap: Liverpool's dramatic win over Borussia Dortmund|
|'One of the greatest Liverpool comebacks - ever!'|
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Villarreal, nicknamed the Yellow Submarine, are fourth in the La Liga table behind Real Madrid, Atletico Madrid and Barcelona.
The draw means that four Spanish clubs could contest both the Champions League and Europa League finals after Real Madrid and Atletico Madrid were kept apart in Europe's elite competition.