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The Italians will take on Bayer Leverkusen, who overcame AS Roma, in their first European final in Dublin on May 22.
Sevilla, the undisputed kings of the Europa League, have now won all seven of the finals they have played in the competition, and are well-versed in the drama of the occasion, having seen their opponents score first in the last four finals
Dybala will become Roma's fourth signing of the transfer window after the arrivals of midfielder Nemanja Matic, goalkeeper Mile Svilar and defender Zeki Celik.
With this win, Jose Mourinho became the first manager to win a European trophy with four different clubs.
Roma confirmed the 40 million euro ($47.08 million) deal for the 23-year-old, who joins Jose Mourinho's team in search of game time.
Villarreal face Arsenal in the other semi after the Gunners thrashed Slavia Prague 4-0 away to complete a 5-1 aggregate victory.
Liverpool agreed to pay the 25-year-old 72.5 million euros, which eclipses the previous record of 53 million euros paid by Juventus for Gianluigi Buffon in 2001.
Real's win thanks to second-half goals from Gareth Bale and Lucas Vazquez means the European champions are guaranteed to top the group due to a better head-to-head over the hosts.
English Premier League side Liverpool FC also tweeted in solidarity and asked its fans to help the victims of the flood-hit state.
Five-time winners Sevilla made light work of AS Roma when first half goals from Sergio Reguilon and Youssef En-Nesyri gave them a 2-0 win.
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