Former European champions PSV were drawn against Belgian debutants Zulte Waregem, while Luciano Spalletti's men will face Nordsjaelland, who finished bottom of a group including Chelsea, Shakhtar Donetsk and Juventus in last season's tournament.
Basel, Europa League semi-finalists in 2012-13, will face either Hungarian side Gyori or Israeli club Maccabi Tel-Aviv, while French giants Lyon will be tested by Swiss team Grasshopper.
Fenerbahce have been drawn against Austrian opponents Salzburg ahead of the Court of Arbitration for Sport's final decision over Uefa's two-year ban from European competition.
Celtic, who beat Barcelona in the competition last campaign, will face either Elfsborg or Daugava Daugavpils should they hold on to their lead over Cliftonville in the second leg of the second qualifying round.
The opening legs will be played on July 30 and 31, with the return games on August 6 and 7.
|CL THIRD QUALIFICATION ROUND DRAW
|Nordsjaelland (NOR)||VS||Zenit St Petersburg (RUS)|
|Salzburg (AUT)||VS||Fenerbahce (TUR)|
|PAOK (GRE)||VS||Metalist Kharkiv (UKR)|
|PSV (NED)||VS||SV Zulte Waregem (BEL)|
|Olympique Lyonnais (FRA)||VS||Grasshopper Club (SUI)|
|Basel (SUI)||VS||Gyori (HUN)/Maccabi Tel-Aviv (ISR)|
|Sligo Rovers (IRL)/Molde (NOR)||VS||New Saints (WAL)/Legia Warszawa (POL)|
|Slovan Bratislava (SVK)/Ludogorets (BUL)||VS||Shirak (ARM)/Partizan (SRB)|
|Dinamo Tbilisi (GEO)/Streymur (FRO)||VS||Steaua Bucharest (ROU)/Vardar (MKD)|
|APOEL (CYP)||VS||Birkirkara (MLT)/Maribor (SVN)|
|Celtic (SCO)/Cliftonville (NIR)||VS||Elfsborg (SWE)/Daugava Daugavpils (LVA)|
|BATE (BLR)/Shakhter Karagandy (KAZ)||VS||Neftci PFK (AZE)/Skenderbeu (ALB)|
|Austria Vienna (AUT)||VS||Ekranas (LTU)/Hafnarfjordur (ISL)|
|HJK Helsinki (FIN)/Nomme Kalju (EST)||VS||Viktoria Plzen (CZE)/Zeljeznicar (BIH)|
|Fola Esch (LUX)/Dinamo Zagreb (CRO)||VS||Sheriff (MDA)/Sutjeska (MNE)|