The Gunners are now just one win away from Champions League qualification, while manager Unai Emery can make history by winning a record fourth Europa League crown.
Trailing 3-1 from the first leg in London, Kevin Gameiro's close-range effort had given the hosts the early impetus. The win means Arsenal, whose first away game of this Europa League campaign was in Azerbaijan against FK Qarabag, will return to the country for the final on 29th of this month.
This will be Arsenal's first European final since 2006 when they lost against Barcelona in the Champions League final.
Elsewhere, Chelsea battled to the final after beating Frankfurt 4-3 on penalties to set up another all English final in Europa League after Tottenham and Liverpool set up all English final in the champions league.