An entertaining clash in front of 60,063 at the Emirates went to extra-time before Pauline Bremer decided the match in the final minute with penalties on the horizon.
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With Arsenal hearts broken and exhausted, coach Jonas Eidevall arranged a post-match team huddle demonstrating the spirit in the squad after an incredible effort over two legs, which ended 5-4 on aggregate.
In front of a sell-out crowd at the Emirates, there were high hopes that the Gunners could go on to reach the final of the Champions League.
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And the north London stadium were sent into a frenzy when Stina Blackstenius came out on top of a defensive error to tuck home the opener on Monday evening.
But Jill Roord, who played for Arsenal for two years, thrashed in an equaliser when the home defence failed to clear a set-piece.
Wolfsburg survived a VAR scare straight after half-time when Blackstenius scored but Noelle Maritz was given offside in the build-up.
That appeared to wake up the German side, who revved up the pressure and took a deserved lead when club captain Alexandra Popp nodded in from a corner.
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But the drama did not stop there when Arsenal drew level after a fantastic header from Jen Beattie, sending the Emirates crowd into raptures again.
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The celebrations were somewhat muted just moments later, though, when Laura Wienroither had to be stretchered off.
It saw the teenage Kathrine Kuhl come on as Eidevall's problems in the physio room mounted up.
Even extra-time could not quell the noise inside the Emirates as Arsenal went up a level, even having the ball in the Wolfsburg net before the referee had already blown up for a foul.
But Pauline Bremer broke Arsenal hearts in the final minute of extra-time after a calamitous mistake at the back.
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Lotte Wubben-Moy was guilty of dallying on the ball as Jule Brand pounced on the error before sliding in Bremer for a tap-in.
It means they will face Barcelona in the Champions League final, a side that have improved exponentially in recent years in the competition.
This is their fourth final in five years, winning twice and will take on a Wolfsburg side that are used to glory in the tournament.
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The German side have won it twice before in 2013 and 2014, reaching the final in 2016, 2018 and 2020.
Arsenal, meanwhile, have won the Champions League once in their history in 2007, which was also the only time they had reached the final.