Former European champions Celtic and Steaua Bucharest will begin their UEFA Champions League journeys against Stjarnan and AS Trencin respectively.
The draws for the first and second qualifying rounds were held on Monday - just 16 days after Barcelona lifted 2014-15 title - with the Scottish champions facing Urvalsdeild winners Stjarnan, who overcame Motherwell in Europa League qualifying last season.
Ronny Deila's side will host Stjarnan in the first leg of the second qualifying round on the July 14 or 15 before playing the return match the following week.
Celtic failed to qualify for last season's tournament despite earning a reprieve after losing to Legia Warsaw, who fielded an ineligible player.
Deila's men then lost to Maribor and went into the Europa League, where they were knocked out by Inter in the round of 32.
Steaua - European champions in 1986 - will travel to Slovakia to face Trencin before returning to Bucharest, having bowed out of last season's qualifiers to Ludogorets in the play-off round.
The Bulgarian side made the headlines as a result, with defender Cosmin Moti going in goal following Vladislav Stoyanov's red card before saving two penalties in the shootout to send his side through.
Ludogorets took four points off Basel and Liverpool before exiting the group stage and will face Milsami Orhei in the second qualifying round this term.
Champions League regulars APOEL and BATE Borisov will play Vardar and Dundalk respectively.
First qualifying round:
Lincoln Red Imps v Santa Coloma
Crusaders v Levadia Talinn
Pyunik v Folgore
B36 Torshavn v The New Saints
Second qualifying round:
Hibernians v Maccabi Tel Aviv
APOEL v Vardar
Qarabag v Rudar Pljevlja
Sarajevo v Lech Poznan
Maribor v Astana
BATE Borisov v Dundalk
HJK Helsinki v FK Ventspils
Midtjylland v Lincoln Red Imps or Santa Coloma
Molde v Pyunik or Folgore
Malmo v Zalgiris Vilnius
Celtic v Stjarnan
AS Trencin v Steaua Bucharest
Partizan v Dila Gori
Ludogorets v Milsami Orhei
Fola Esch v Dinamo Zagreb
Skenderbeu v Crusaders or Levadia Talinn
B36 Torshavn or The New Saints v Videoton
