The Spanish club won the second leg 4-1 at the Vicente Calderon in Madrid to clinch the last-16 tie, having triumphed 1-0 in the first leg in Italy last month.
Diego Costa broke the deadlock for Atletico as early as the third minute with an acrobatic effort from close range after Koke had put in a good delivery from the right.
Kaka scored the equaliser for Milan on 27 minutes when he headed home Andrea Poli's cross past Thibaut Courtois.
However, the Italian giants' hopes of a comeback were extinguished five minutes before the break when Arda Turan's shot from outside the box was deflected into the net.
Raul Garcia found the target with a close-range header in the 70th minute, and with five minutes of normal time remaining, Costa added his second goal of the evening to wrap up the victory.
Atletico headed into the game as one of only two sides still unbeaten in this season's competition, having won 15 of their last 16 home games in Europe.
Form favoured the Rojiblancos and after just three minutes Diego Simeone's side went ahead. Koke floated in a cross from the right edge of the area and Costa, having peeled away from Milan centre-back Adil Rami, flung himself at the ball and managed to volley it past Christian Abbiati at full stretch.
That was Costa's sixth goal in this season's Champions League and 27th in all competitions and, of more immediate significance, it left Milan needing to score at least three times to go through.
Glimmer of hope
However, the Rossoneri got a foothold back into the tie in the 27th minute when Kaka headed home from their first decent opportunity.
Mario Balotelli played the ball out to Poli and his deep cross was met at the far post by the Brazilian, whose header flew into the net via the thigh of Atletico defender Juanfran.
That was just the boost Milan needed and they really should have taken a 2-1 lead in the 36th minute, but this time Kaka contrived to head a great chance over from six yards.
The Brazil international really should have scored from that, but Atletico survived and four minutes later they were ahead again, albeit with the help of a huge slice of good fortune.
Costa chested the ball down to Turan on the edge of the area and the Turkish midfielder's half-volley took a crucial deflection off Rami before looping into the net.
The momentum was back with the Spanish side now and Garcia almost made it 3-1 with a spectacular overhead kick just before the break, the ball going inches wide with Abbiati rooted to the spot.
Atletico were back on the attack after the interval with recent Spain debutant Costa and Gabi going close before Milan substitute Robinho - another Real Madrid old boy - drew a parry out of Courtois with a cross-shot.
Milan were pushing but they could not find a breakthrough before Atletico all but settled the tie in the 71st minute when Garcia climbed above two visiting defenders to head home Gabi's free-kick.
There was no way back for Clarence Seedorf's men after that, although Robinho did hit the crossbar soon after, and Atletico wrapped up a convincing win when Costa drilled a shot in off the far post in the 85th minute.