The first leg of the tie ended goalless at the Emirates Stadium, leaving the Gunners with a massive task on their hands, but they roared through thanks to goals from Cesc Fabregas and Emmanuel Adebayor.
The opening minutes saw little of either sides' attack, before Alexandre Pato beat a couple of defenders and earned a corner, which was almost deflected into his own net by Adebayor.
Five minutes later, Adebayor held the ball up superbly and fed the arriving Abou Diaby and he curled a right-foot shot narrowly wide from 20 yards out.
Kaka, who was kept quiet for much of the game, raced away from a couple of markers after 19 minutes and floated a delightful chip over the defence to Pato at the far post, but his tame shot was straight at Manuel Almunia.
Just before the half-hour mark, Adebayor made a yard of space on the left side of the area and his dipping shot forced Zeljko Kalac into a tip-over at full stretch.
Five minutes later, Adebayor caused problems again and his pass to Fabregas allowed the Spaniard to fire off a swerving shot, which beat Kalac before smacking against the crossbar.
Early in the second half, Andrea Pirlo gave the ball away to Adebayor on the edge of the Milan area, he played in Emmanuel Eboue, but he sliced his shot wide of Kalac's near post.
After that the game started to open up a little, but it wasn't until 16 minutes from time that another clear opening was created.
Alexander Hleb played a superb ball over the top to sub Theo Walcott, his cross was half-blocked and, as Adebayor went for the rebound, Kalac dived to gather the loose ball.
Six minutes from time the Gunners struck the crucial first goal as Fabregas turned past Gennaro Gattuso and his low 35-yard right-foot shot somehow crept past Kalac into the corner of the net.
That left Milan needing two goals to rescue the game, but their misery was complete in stoppage time as Arsenal wrapped up the tie with a superb second goal of their own.
Walcott did superbly on the right and drove on towards the by-line, before squaring the ball across the area for Adebayor to net from close range to seal a well-deserved 2-0 win on the night and on aggregate.