Juergen Klopp's Liverpool came from 3-1 down against Dortmund to win 4-3 with a goal in stoppage time that secured a 5-4 aggregate success.
They will now travel to Spain for the first leg against Villarreal, who are fourth in La Liga, on April 28 with the return at Anfield on May 5.
The Spanish side owe their nickname, Yellow Submarine, to Liverpool's most famous sons, The Beatles.
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They have a terrible record playing against Premier League opposition, however, and are without a win in their last 10 games against English sides.
Liverpool, despite their struggles in the Premier League this season, will begin as favourites as they bid to reach a 12th European final, meeting a Villarreal side who have never contested a single one.
"Liverpool are used to winning trophies, we’re going to experience a very special atmosphere there," former Spain and Villarreal midfielder Marcos Senna said.
Sevilla, who are bidding for a record third straight Europa League title, will play Shakhtar, who lifted the trophy in 2009.
The holders, who beat fellow Spaniards Athletic Bilbao on penalties in the quarter-final, will have home advantage for the second leg.
The tie gives Shakhtar coach Mircea Lucescu an opportunity for revenge after the Ukrainians were beaten by Sevilla in the last 16 of the UEFA Cup nine years ago when the Spanish side's keeper Andres Palop headed a 94th-minute equaliser.
Sevilla won the tie in extra time and went on to win.
"I don't think about that game anymore," Lucescu said. "We will try to take revenge, but it will be very difficult."
The final will take place in Basel on May 18.
(Reporting by Steve Tongue and Toby Davis; Editing by Louise Ireland)
