With a 3-0 lead over Fenerbahce from the first leg, Aaron Ramsey netted twice to ensure Arsenal comfortably won the playoff 5-0 on aggregate.
"At the top level, the most difficult thing is to be consistent and of course it's an achievement," to qualify again, manager Arsene Wenger said, "but our ambition is much higher than that."
Arsenal has never won European football's biggest prize or any trophy since the 2005 FA Cup.
It was a nervier night for Schalke, which overcame U.S. midfielder Jermaine Jones being sent off to win 3-2 at Salonika and advance 4-3.
Steaua Bucharest will be in the group stage for the first time in five years after drawing 2-2 at Legia Warsaw to go through on away goals after the first leg finished 1-1.
Basel, already leading Ludogorets Razgrad 4-2, won 2-0 on home soil to cruise into Thursday's draw where it will be joined by Austria Vienna, which squeezed through 4-3 on aggregate despite losing 3-2 at home to Dinamo Zagreb.
In London, Fenerbahce gifted Arsenal the lead after 25 minutes, with Ramsey providing the finish from close range.
The Wales midfielder, who scored in Istanbul last week, volleyed in another in the 72nd after being set up by Kieran Gibbs.
There had been a blow for Arsenal early in the second half when Lukas Podolski was carried off on a stretcher with a left hamstring injury that is expected to sideline the Germany forward for three weeks.
"We paid a heavy price on the injury front," Wenger said.
The result ended concerns about the chaos awaiting UEFA if Fenerbahce advanced while appealing a two-year Champions League expulsion over a 2011 Turkish match-fixing case. That appeal verdict from the Court of Arbitration for Sport is scheduled for Wednesday.
In Greece, Adam Szalai put Schalke in front before half time after Atsuto Uchida squared the ball to him.
Stefanos Athanasiadis blasted in an equalizer for the resilient Salonika at the start of the second half, and their chances of advancing appeared to have been boosted by Schalke being reduced to 10 men when Jones received his second booking for fouling Dimitris Salpingidis in the 64th.
But after an exchange of goals, Szalai struck again in the 90th to ensure Schalke will play in the group stage for the sixth time.
In Poland, Steaua appeared to be cruising after Nicolae Stanciu and Federico Piovaccari scored inside the first nine minutes to put the visitors 3-1 up on aggregate
Legia Warsaw pulled one back in the 27th through Miroslav Radovic's header and Jakub Rzezniczak netted in the fourth minute of stoppage time, but it came too late to prevent Steaua progressing on away goals.
Basel enjoyed the most relaxing outing, with Fabian Frei knocking in a corner after 11 minutes and substitute Philipp Degen scoring with his second touch 11 minutes from the end.