New manager Ronny Deila will face the champions of Iceland at home on July 15 or 16 in his first competitive game in charge of the Glasgow club.
The first leg is set to be played at Murrayfield as Parkhead will play host to the Commonwealth Games, with the return fixture played on either July 22 or 23.
Deila, who was appointed as Neil Lennon's successor after the Northern Irishman resigned last month, will be expected to see Celtic through against a Reykjavik side who sit fourth in the Icelandic top flight.
Former European champions Steaua Bucharest face Stromsgodset IF of Norway in the second qualifying round and the Romanian outfit will have home advantage in the second leg.
Lincoln Red Imps will become the first club from Gibraltar to participate in the Champions League when they lock horns with Faroe Islands club HB Torshavn in the first qualifying round - with the first leg played on either July 1 or 2.
The winner of the clash between those two minnows have the incentive of taking on Partizan Belgrade in the second qualifying round.
Israeli champions Maccabi Tel Aviv lie in wait for the winner of the first qualifying round tie between Andorran champions FC Santa Coloma and Armenian club FC Banants.
Estonian club FC Levadia Tallinn and SP La Fiorita of San Marino meet in the other first qualfying round tie.
Champions League first qualifying round draw in full:
FC Santa Coloma v FC Banants
Lincoln Red Imps v HB Torshavn
SP La Fiorita v FC Levadia Tallinn
Champions League second qualifying round draw in full:
BATE Borisov v KS Skenderbeu
Maccabi Tel-Aviv v FC Santa Coloma or FC Banants
Dinamo Tbilisi v FC Aktobe
HSK Zrinjski Mostar v NK Maribor
FC Sheriff v FK Sutjeska
AC Sparta Praha v SP La Fiorita or FC Levadia Tallinn
Malmo FF v FK Ventspils
SK Slovan Bratislava v The New Saints
Celtic v KR Reykjavik
Cliftonville v Debreceni VSC
Partizan Belgrade v Lincoln Red Imps or HB Torshavn
Legia Warsaw v Saint Patrick's Athletic
FK Rabotnicki v HJK Helsinki
Dinamo Zagreb v VMFD Zalgiris
PFC Ludogorets 1945 v F91 Dudelange
Valletta v Qarabag FK
Stromsgodset Toppfotball v Steaua Bucharest
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