Unai Emery's side will face Chelsea in Baku on May 29 after their London rivals beat Eintracht Frankfurt on penalties to ensure both European club competitions will feature all-English finals.
Arsenal's first win on Spanish soil since beating Real Madrid at the Bernabeu in 2006 kept their hopes of qualifying for next season's Champions League through Europe's secondary competition alive.
"We reacted well to going behind and we knew we had to score a minimum of one goal tonight," Lacazette told BT Sport.
"Auba (Aubameyang) was unbelievable tonight with an incredible hat-trick, so thanks to him.
"We have played badly in the Premier League during the last month and now we have to use this opportunity. We want to play in the Champions League next season and we want the trophy."
In a week of improbable European comebacks, Valencia, trailing 3-1 from the first leg, were seeking to become the latest side to overturn a hefty deficit and made the perfect start as Kevin Gameiro slid in to convert Rodrigo's centre with 11 minutes played.
Rodrigo sent an effort wide as the home crowd sensed an upset, but Arsenal were soon level when Aubameyang notched his first out of nothing, producing a fine finish from outside the box from Lacazette's flick on following goalkeeper Petr Cech's long clearance.
Valencia continued to push forward, with Dani Parejo sending a free kick narrowly wide before Jose Luis Gaya was booked for diving on the cusp of halftime as they desperately sought a second.
Marcelino's side were caught napping by Lacazette's curling effort just after the break to put the visitors ahead on the night.
Gameiro converted Rodrigo's mis-hit shot just before the hour to set up a possible grandstand finish, but Aubameyang soon restored Arsenal's lead before completing his treble two minutes from time to book their first European final since they lost the 2006 Champions League final to Barcelona.
Tempers flared as players from both sides clashed on the final whistle, but it was Emery's side celebrating as they booked their final place.
Liverpool will play Tottenham Hotspur in the Champions League final in Madrid on June 1.
(Reporting by Joseph Cassinelli, editing by Ed Osmond)
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