The Londoners had salvaged a 1-1 draw late in the first leg at the Emirates last week, but were undone by goals in each half from the Frauen-Bundesliga leaders.
Former Gunner Jill Roord scored the opener after just nine minutes, hooking in from close range after the visitors failed to clear a corner.
The home side – playing at the men’s team’s Volkswagen Arena – thought they had netted again when Tabea Wassmuth stroked in but after a long check by VAR, it was ruled out for offside.
They did get a fortuitous second on 72 minutes when defender Leah Williamson inadvertently converted into her own net from Sveindis Jane Jonsdottir’s low cross.
Arsenal pushed to find a way back into the tie but Vivianne Miedema’s towering header struck the crossbar, before Williamson’s follow-up was brilliantly tipped onto the post by goalkeeper Almuth Schult.
“We could have played better in the first half,” said Gunners manager Jonas Eidevall. “We knew it would be a game of fine margins and it was, but we hit the bar, the post and they didn’t go our way.
“They are very physical and demand a lot of opponents. I’m a little disappointed with certain aspects of our performance.
“They man-marked us and were very aggressive. We expected that but we were disappointed we didn’t find the tactical balance.”
Victory for two-time champions Wolfsburg sets up a tantalising semi-final against current holders Barcelona.
The Spanish champions progressed on Wednesday following an 8-3 aggregate win over rivals Real Madrid, a match played at the Nou Camp in front of a world record crowd of 91,553.
‘We need to improve to go further’
Back-to-back winners of the competition in 2012-12 and 2013-14, Wolfsburg highlighted why they are top of the table in Germany by ousting the last remaining English side.
Tommy Stroot’s team are locked in a tense title tussle, one point clear of Bayern Munich, while Arsenal themselves are fighting for the WSL crown, a point adrift of leaders Chelsea.
Though they still have an FA Cup semi-final to come next month against the Blues, their exploits in Europe came to an end for another campaign.
Arsenal won the trophy for the only time in 2007 and last reached the semi-finals nine years ago.
Captain Kim Little said her side had played well “at times” during both legs but “not for long enough”, adding that they needed to learn to keep the ball better to compete at this level.
“We’ve progressed a lot since the last time we were at this stage in the Champions League against PSG [in 2020].
“But we still now can see we’ve got a little bit more to go to be able to compete and win in these later stages of the Champions League.”
Kick-off in Germany was delayed by five minutes to clear confetti which had fallen on the pitch and ultimately it was Wolfsburg that were left celebrating in style.
They made the best possible start when Roord spun and converted inside the first 10 minutes and were much the better side in the opening period.
Jonsdottir fired over from the edge of the area and another cross from the left almost sailed in but was tipped over by Manuela Zinsberger.
The Arsenal goalkeeper was being kept busy and also made a sharp save to deny Svenja Huth’s low drive.
They did eventually double their advantage in the second period with a helping hand from Williamson, poking in an own goal in between the legs of her team-mate.
At the other end, Miedema was on the periphery of the contest, hooking a shot over from an acute angle, while the Netherlands international was unable to turn home after Schult spilled a cross.
She came close to pulling a goal back when she struck the crossbar and, had that gone in, the tie would have seen a grandstand finish, but Wolfsburg comfortably saw the game out
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