Aaron Ramsey stole the show at the Emirates Stadium by grabbing both goals, wrapping up a comfortable 5-0 aggregate triumph.
Arsenal dominated possession in the first half and Ramsey was on hand to tap home from six yards in the 25th minute.
Theo Walcott then hit the crossbar from a free-kick before Ramsey’s volley made it 2-0.
Boss Arsene Wenger made two changes to the side that beat Fulham 3-1 on Saturday with Jack Wilshere and Nacho Monreal replacing Tomas Rosicky and Kieran Gibbs.
Fenerbahce, meanwhile, included former Liverpool players Raul Meireles and Dirk Kuyt.
Arsenal dominated the early possession but they almost conceded a goal in unusual circumstances.
A scramble in the box led to Bacary Sagna clearing his effort straight against Meireles, with the ricochet drawing a smart save from Wojciech Szczesny.
The home side then fashioned their first chance with a swift counter-attack.
Santi Cazorla burst through two challenges and laid the ball to Wilshere whose pass found Olivier Giroud, but the Frenchman curled his effort wide from 20 yards.
Arsenal continued to probe and their pressure finally yielded a breakthrough in the 25th minute.
Gokhan Gonul tried to prevent Lukas Podolski's throughball from finding Walcott, but his sliding challenge went straight to Ramsey, who swept the ball home.
Giroud then came close to doubling the advantage seven minutes later when his shot from a narrow angle forced Volkan Demirel into a smart save with his legs.
Fenerbahce almost caught Arsenal out when Emmanuel Emenike broke free on the left and unleashed a fierce drive that Szczesny pushed against the post before Giroud found himself in space, only to fire over from six yards after an excellent low cross from Cazorla.
Podolski was withdrawn from the action a minute into the second half when he pulled up with what looked like a hamstring injury.
His removal temporarily stunted Arsenal's momentum, and Egemen Korkmaz linked well with Emenike for the visitors before crashing an effort off the crossbar, although he would have been denied by the offside flag.
Cazorla almost grabbed the second for Arsenal in the 63rd minute before Walcott dipped a free-kick against the crossbar.
But with 18 minutes left they wrapped up the win when Gibbs broke free before crossing for Ramsey to volley into the corner.
Arsenal were given a late scare when Wilshere went down holding his ankle after a robust challenge from Meireles, but he recovered to finish the game.
