Trailing 3-1 from the first leg, Valencia made the perfect start at Mestalla when Kevin Gameiro finished at the back post but goals from Aubameyang and Alexandre Lacazette left the home side needing four in 40 minutes.
Gameiro scored again, sparking hopes of a revival to trump even the efforts of Liverpool and Tottenham this week, before Aubameyang hit his second and then completed a brilliant hat-trick to seal a 4-2 win, 7-3 on aggregate.
There will be a London derby for the final in Baku on May 29 and, for the first time in history, four English teams competing in both the Champions League and Europa League finals, with Liverpool and Spurs meeting in Madrid three days later.
It also keeps alive Arsenal's chance of securing a place in the Champions League next season and, realistically, their last chance, given they need to overturn three points and an eight-goal swing on Tottenham in the Premier League this weekend.
"We couldn't get the Champions League through the league, but this is another way," said Arsenal coach Unai Emery. "Our objective is clearly to go to the Champions League but also this is a trophy. It will not be easy."
Valencia had been relying on the Europa League for Champions League qualification too, given they sit three points behind Getafe, who face a demoralised Barcelona on Sunday, with two games left in La Liga.
But over the two legs, Marcelino's side could have few complaints. They were second best at Emirates Stadium and defensively frantic here.
Arsenal, usually so fragile away from home, picked them off with ease as Aubameyang and Lacazette, boasting 48 goals between them this season, proved themselves to be a first-class attack in a second-tier competition.
"Auba was unbelievable tonight," Lacazaette told BT Sport. "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."
There will also be no Spanish team in either European final for the first time since 2013, and only the second time in 10 years.
Valencia made a brilliant start as Jose Gaya headed wide at the near post and Goncalo Guedes fired over, with Petr Cech playing for time as early as the fifth minute in the hope of a chance for breath.
Instead, Arsenal conceded, caught upfield after Alex Maitland-Niles shot at Neto, who rolled out to launch the counter-attack. Rodrigo swept wide to Guedes and ran ahead of him, receiving and firing to the back post, where Gameiro slid in.
Valencia looked like they could score six let alone the one more required, only for Arsenal to find an equaliser against the run of play.
Cech punted downfield and Lacazette flicked on, with Aubameyang nipping in and, before his opponents could recover, driving into the bottom corner.
The rest of the half was high on intensity but low on quality as Valencia struggled to reboot. Aubameyang shot at Neto and Lacazette's whipped effort clipped the outside of the post.
Half-time should have been timely for the hosts but it was Arsenal that scored shortly after.
Dani Parejo's careless pass put them in trouble before Gaya was outmuscled. Lucas Torreira found Lacazette, who spun out of the clutches of Cristiano Piccini and buried the ball into the corner.
The tie looked done, Valencia needing four in 40 minutes, but they got one back eight minutes later, Gameiro diverting Rodrigo's shot in after Daniel Wass had cut back.
Valencia believed again but only briefly because Aubameyang struck again. Maitland-Niles ghosted past Guedes and crossed to the near post, where Aubameyang was too quick for Gabriel Paulista.
Some of Valencia's fans headed for the exits and even more followed when Aubameyang lashed another shot into the roof of the net for his third, and Arsenal's fourth.
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