Marc Skinner's Reds completed a two-legged victory over Norwegian side Brann in the final round of qualifying on Thursday, to advance to the competition's main stage for the first time.
In Friday's draw, it was announced we'll play home matches against French giants Lyon and Paris Saint-Germain, plus Norwegian champions Valerenga of Oslo.
Trips to Spanish outfit Atletico Madrid, Italian title-holders Juventus and German side Wolfsburg also feature on the six-game slate for United.
The home tie with Valerenga will kick things off on Wednesday 8 October, before the visit to Atletico Madrid just over a week later, on the following Thursday.