The Gunners were already leading the Italian side 2-0 from the first leg and managed to progress 5-1 on aggregate with an impressive home win.
There was a scare for the hosts at the Emirates when Hakan Calhanoglu scored for AC Milan. But Danny Welbeck levelled things up from the spot minutes later after winning a controversial penalty.
Granit Xhaka and another from Welbeck completed a 3-1 win on the night.
Arsene Wenger’s side can now look forward to Friday’s draw in which they will discover which side they will face for a place in the semi-finals.
Who could they face?
How did the remaining sides make it through to the quarter-finals?
Round of 16 results
Atletico Madrid beat Lokomotiv Moscow 8-1 on aggregate.
Marseille beat Atletico Bilbao 5-2 on aggregate
Lazio beat Dynamo Kiev 4-2 on aggregate
RB Leipzig beat Zenit St Petersburg 3-2 on aggregate
Sporting Lisbon beat Viktoria Plzen 3-2 on aggregate
Arsenal beat AC Milan 4-1 on aggregate
Red Bull Salzburg beat Borussia Dortmund 2-1 on aggregate
CSKA Moscow beat Lyon on away goals after their tie ended 3-3 on aggregate
Which teams will Arsenal want to avoid?
Atletico Madrid are arguably the standout team remaining, with Diego Simeone’s side currently second in La Liga and dismantling Lokomotiv Moscow 8-1 in the Round of 16.
Lazio, who are fourth in Serie A, could prove tricky.
However Borussia Dortmund, who many fancied to do well in the competition, are out after failing to overturn their 2-1 first leg defeat to RB Salzburg.
Exactly when is the quarter-final draw?
For full details on the draw, click here.