English football's two representatives will compete over two legs for the right to face either Tyreso of Sweden or Austria's Neulengbach in the semi-finals.
Arsenal reached the quarter-finals with a 6-2 aggregate victory over Glasgow City, while Birmingham bear Russians FK Zorkiy 7-2 over two legs.
Birmingham boss David Parker told Sky Sports News: "We've achieved beyond all expectations - and reaching the quarter-finals is the icing on the cake.
"I think there's a little bit of disappointment on both sides - being in the last eight you want to go abroad and experience different levels of football - and we've played Arsenal numerous times over the last couple of years.
"It would have been better in the semi-final so we could have guaranteed an English club in the final."
Arsenal boss Shelley Kerr said: "I think we'd rather have met Birmingham further on in the competition - but it's fewer miles to travel! In the previous round we had to travel to Kazakhstan, so it's a bit closer now.
"The women's game has evolved so much and at this level the teams are so tough to play against - we're delighted to be in the last eight so we'll just have to wait and see what happens."
Elsewhere the draw pitted holders Wolfsburg with Barcelona, and the winners of that tie will meet either Italian side Torres or Germany's Turbine Potsdam in the last four.
Quarter-final ties will take place in the final two weeks of March, with the semi-finals in the final two weeks of April and the Lisbon final scheduled for May 22.
Tyreso v Neulengbach
Wolfsburg v Barcelona
ASD Torres v Turbine Potsdam
Birmingham v Arsenal
Birmingham/Arsenal v Tyreso/Neulengbach
Torres/Potsdam v Wolfsburg/Barcelona