The first leg is to be played on the 5 April with the reverse fixture to be played a week later, on 12 April.
Arsenal qualified for the quarter-finals after cruising past AC Milan in the Round of 16 stage and Swedish side Ostersund in the last 32.
Arsenal last reached a European quarter-final in 2010, when they lost to Barcelona in the Champions League.
The Gunners look unlikely to secure a top-four finish in the Premier League, currently sitting in sixth place - 12 points behind fourth-spotted Liverpool.
Arsene Wenger's men, though, have now won their last three matches in all competitions to ease the pressure a little on the veteran Frenchman.
In the other quarter-final ties, Atletico Madrid face Sporting Lisbon, RB Leipzig tackle Marseille and Lazio take on Red Bull Salzburg.