The Gunners took their chances in the first leg to lead 3-1 at the midway stage and they were equally as clinical in Spain on Thursday night, scoring from four of their five shots on target.
Arsenal will now face Premier League rivals Chelsea in the Baku final in three weeks' time following the Blues' penalty-shootout win against Eintracht Frankfurt in the other semi-final.
Rodrigo Moreno made the most of the space down the left by carrying the ball forward and crossing for Gameiro to convert at the back post.
Los Che started the match in an attacking manner and nearly had a second, only for Gameiro to block Rodrigo's shot in front of goal.
Against the run of play, though, and from their first serious attack of the night, Lacazette flicked the ball on for Aubameyang to send it spinning past Neto with the outside of his boot.
Aubameyang tested Neto soon after and Goncalo Guedes sent a free kick marginally wide of the post, but it was Arsenal who came closest to scoring a second before half time as Lacazette skimmed the outside of the post from 10 yards after being teed up by Aubameyang.
Arsenal did grab the goal that killed off the tie five minutes into the second period thanks to another fine finish, this time from Lacazette as he dragged the ball away from Cristiano Piccini and picked out the bottom corner from 15 yards.
Los Che refused to give up, however, and they gave themselves a glimmer of hope when Gameiro bundled the ball over the line just before the hour mark after again blocking Rodrigo's shot in front of goal.
Continuing the theme of clinical finishing across the two legs, Aubameyang converted Maitland-Niles' front-post cross from just inside the six-yard box to restore Arsenal's four-goal cushion.
Aubameyang completed his hat-trick two minutes from time with a thumping finish into the roof of the net after exchanging passes with substitute Henrikh Mkhitaryan, sending Arsenal through to their first European final in 13 years.
VALENCIA (4-4-2): Neto; Piccini (Soler 56'), Garay, Gabriel, Gaya; Wass, Parejo, Coquelin, Guedes (Torres 71'); Moreno (Mina 71'), Gameiro
ARSENAL (3-4-1-2): Cech; Sokratis, Koscielny, Monreal; Maitland-Niles, Torreira (Guendouzi 80'), Xhaka, Kolasinac (Mustafi 71'); Ozil (Mkhitaryan 62'); Aubameyang, Lacazette