Jonas Eidevall's side had it all to do at Meadow Park following a 1-0 defeat in last week's first leg, but as expected, the Gunners reverted to type on familiar territory to send their Swedish foes packing with a 4-0 second-leg win.
Lia Walti, Mariona Caldentey, Beth Mead and Frida Maanum were all on target for the rampant hosts at Borehamwood, as Arsenal banished the demons of last year's preliminary exit to Paris FC and confirm their rightful place among the European elite.
Walti was omitted from the starting XI for the weekend's thrilling 2-2 Women's Super League draw with Manchester City, but the Swiss midfielder justified her return to the first XI with a stunning opener just 23 minutes in.
The 31-year-old let fly with a first-time left-footed strike from around 25 yards out, which dipped awkwardly for Hacken goalkeeper Jennifer Falk, who could only palm the ball onto the underside of the crossbar and into the back of the net.
The Gunners bagged the insurance goal five minutes before the break thanks to a defensive calamity from Hacken, who failed to deal with a heavy touch from Mead, and the ball fell kindly for Caldentey to finish thanks to a wicked deflection off of Emma Ostlund.
Picking up where they left off at the end of the first half, Arsenal capitalised on more lackadaisical defending from their visitors to increase their lead in the 49th minute, as Mead expertly flicked the ball up before hooking a terrific volley into the bottom corner.
Maanum came off the bench to add some gloss to the scoreline towards the end, latching onto a Caitlin Foord cutback and slotting in the hosts' final effort of a historic evening for English clubs.
As well as Arsenal's triumph, Manchester City thumped Paris FC 8-0 on aggregate to join the Gunners and Chelsea in the group stage, which will feature three Women's Super League teams for the first time ever.
When is the Women's Champions League group-stage draw?
The 16 teams involved in the Women's Champions League group stage will learn their fate on Friday lunchtime, when the draw is held at 12pm UK time at UEFA's headquarters in Nyon, Switzerland.
Arsenal will be pot two for the draw alongside Wolfsburg, Real Madrid and Man City, while Chelsea, Lyon, Bayern Munich and reigning champions Barcelona are in pot one.
Meanwhile, Roma, St Polten, Juventus and FC Twente make up pot three, as Celtic, Valengra, Hammarby and Galatasaray enter the draw in pot four.