The Gunners won 3-0 in Turkey last week and made it even more difficult for Fener when Aaron Ramsey, who scored in the first leg, put the aggregate beyond doubt in the 25th minute.
Ramsey, who suffered a horrific broken leg a few years ago, feels he is now getting back to his best-ever form.
"I'm enjoying myself out there and I'm confident out there. After the injury I had to take a bit of time to get over it mentally and I think that's ending now," he told ITV.
"I'm starting to enjoy myself and to show people what I'm capable of doing."
Ther triumph has allowed Arsene Wenger's Gunners side to contest Europe's premier club competition for a 16th straight season.