Diego Simeone's men, who won the first leg 1-0, triumphed 4-1 at Vincente Calderon in the return game on Tuesday as goals from Diego Costa and Arda Turan sandwiched Kaka's close-range header in the first half.
Raul Garcia and Costa's second added further gloss to the scoreline inside the final 20 minutes.
The hosts were good value for the victory in an entertaining fixture in the Spanish capital and, with just three points separating them from city rivals Real at the top of La Liga, Simeone's side can now continue their assault on the domestic and European front.
Atletico made the perfect start as Costa – who also scored in the first encounter – was once more the thorn in Milan's defence, stretching athletically to meet Koke's sublime cross to score his sixth Champions League goal in five matches.
Former Real Madrid man Kaka threatened a comeback for Clarence Seedorf's men with a close-range header, but Atletico led at the break in fortunate circumstances courtesy of Turan's deflected volley.
The match was wrapped up on 70 minutes when Raul Garcia leapt to head home Gabi's free-kick, before Costa bagged his brace in the closing stages to send Atletico into the quarters for the first time in 17 years.
The Brazilian then missed a clear chance to put Milan ahead on away goals, as he leapt to meet Adel Taarabt's centre, but succeeded only in heading over from six yards.
That miss proved costly as Turan restored Atletico's lead in fortuitous circumstances five minutes before the break. The Turkey international's volley took a huge deflection off Daniele Bonera before looping over Abbiati and nestling in the bottom corner.
The pressure finally told when the tie was put beyond all doubt 20 minutes from time, as Raul Garcia rose high to nod Gabi's free-kick into the bottom corner.
