The Reds will travel to San Siro on Tuesday 16 February to face a side likely to include former Old Trafford star David Beckham. The second leg will be played in Manchester on Wednesday 10 March.
The sides have met eight times in European competition, most recently at the semi-final stage in the 2006/07 competition when the Italians triumphed 5-3 on aggregate.
Sir Alex said: "We've come up against AC Milan many times in the quarter and semi-finals so it'll be a fantastic setting for two great clubs and we're very much looking forward to it."
Elsewhere, defending champions Barcelona meet Stuttgart, while Jose Mourinho will return to Chelsea with Internazionale. Arsenal were paired with FC Porto.
Stuttgart v Barcelona
Olympiakos v Bordeaux
Internazionale v Chelsea
Bayern Munich v Fiorentina
CSKA Moscow v Sevilla
Olympique Lyonnais v Real Madrid
FC Porto v Arsenal
AC Milan v United
See how events in Nyon unfolded in ManUtd.com's live blog.