The Welsh midfielder's headline-stealing goals saw the Londoners through to the Champions League group stage for the 16th straight season.
Aaron Ramsey stole the show at the Emirates Stadium by grabbing both goals, wrapping up a comfortable 5-0 aggregate triumph, although he limped off with an injury that will be of concern to manager Arsene Wenger.
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 the Welshman's volley made it 2-0.
|By Liam Twomey at the Emirates Stadium
"In the end it was just as easy as everyone assumed that it would be. Arsenal is into the Champions League group stages for the 16th successive season and in some style, albeit against uninspired Turkish opposition.
"Aaron Ramsey was once again the star of the show, breaking from midfield to score twice and add a layer of gloss to a victory which was achieved a week ago in Istanbul.
"Fenerbahce was poor, certainly, but Arsene Wenger's men have now won four in a row. Now if they can just get that 'buying people' thing right..."
Arsenal dominated the early possession but 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 its first chance with a swift counterattack. 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.
The Gunners continued to probe and their pressure finally yielded a breakthrough in the 25th minute. Gokhan Gonul tried to prevent Lukas Podolski's through ball 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Podolski was withdrawn from the action a minute into the second half when he pulled up with what looked like a hamstring injury.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, the Gunners wrapped up the win when Gibbs broke free before crossing for Ramsey to volley into the corner.
Arsenal was given a late scare when Wilshere went down holding his ankle after a robust challenge from Meireles, but he recovered to finish the game. Ramsey, however limped off with an apparent groin injury, putting a damper on his outing.