The winners will progress to the Champions League group stages proper and the losers will drop into the Europa League group stages.
Club Brugge, who were runners-up in the Belgian Pro League last season, beat Panathinaikos 4-2 on aggregate in the previous round but it will be seen as a decent draw for Louis van Gaal’s side, who could have been pitted against Lazio, Monaco or CSKA Moscow.
United have never played Club Brugge but they have a history of meeting Belgian opposition in Europe, including a record 10-0 victory over Anderlecht in the 1956-57 European Cup.
United secretary John Alexander said: “We’re absolutely delighted to be back in the competition. We’re back where we want to be.
“Belgian football is right at the very top and we have two Belgian players in the squad who keep us abreast of what’s going on there. We go into any game with confidence. We’d like to think we can win the competition.”
United will entertain Club Brugge at Old Trafford on Tuesday, August 18 with the return at the Jan Breydel Stadium on Wednesday, August 26.
Full draw for Champions League play-offs
Astana (Kaz) v APOEL (Cyp)
Skenderbeu (Alb) v Dinamo Zagreb (Cro)
Celtic (Sco) v Malmo (Swe)
Basel (Sui) v Maccabi Tel-Aviv (Isr)
BATE Borisov (Blr) v Partizan Belgrade (Srb)
Lazio (Ita) v Bayer Leverkusen (Ger)
Manchester United (Eng) v Club Brugge (Bel)
Sporting Lisbon (Por) v CSKA Moscow (Rus)
Rapid Vienna (Aut) v Shakhtar Donetsk (Ukr)
Valencia (Esp) v Monaco (Fra)