The Scottish champions defeated HJK Helsinki 4-1 across two legs to reach the play-offs and learned their fate at UEFA's headquarters in Nyon on Friday morning.
Helsingborgs are the first Swedish team that Celtic have ever faced in European competition.
The Bhoys will play away from home in the first leg, which will take place on August 22 or 23. The second leg at Parkhead will take place on August 28 or 29.
The two clubs have some common ground as both played host to the extravagant talents of Henrik Larsson.
The former Sweden international played for Helsingborgs from 1992 to 1993 and 2006 to 2009, as well as enjoying seven glorious years in Glasgow between 1997 and 2004.
Elsewhere, Spanish club Malaga, who have been beset by financial problems that forced them to sell star player Santi Cazorla to Arsenal, were drawn against Panathinaikos.
Teams were separated for the draw based on whether they qualified as league champions or not.
Full Champions League play-off draw:
FC Basel (SUI) v CFR Cluj (ROU)
Helsingborgs (SWE) v Celtic (SCO)
BATE Borisov (BLR) v Hapoel Kiryat Shmona (ISR)
AEL Limassol (CYP) v Anderlecht (BEL)
Dinamo Zagreb (CRO) v NK Maribor (SVN)
Braga (POR) v Udinese (ITA)
Spartak Moscow (RUS) v Fenerbahce (TUR)
Malaga (ESP) v Panathinaikos (GRE)
Borussia Moenchengladbach (GER) v Dynamo Kiev (UKR)
Lille (FRA) v Copenhagen (DEN)