The winner between Belfast’s Linfield and SP La Fiorita in the first qualifying round will play Brendan Rodgers’ treble winners, who have been seeded in the draw in Nyon.
Celtic will play away from home first.
Also entering in the first round are Welsh side The New Saints, who will play Gibraltar’s Europa.
Celtic were seeded in Group Three, along with Poland’s Legia Warsaw, Maribor of Slovenia, Swedish outfit Malmo, Rosenborg of Norway and Iceland’s Hafnarfjordur.
The first qualifying round first-leg ties will be on 27 or 28 June with the return legs on 4 or 5 July. The dates for the second qualifying round ties are 11/12 July and 18/19 July.
Last season, Celtic came through the second and third qualifying rounds, and then the play-off round, to reach the group stage, finishing bottom of their section.
Champions League first qualifying round
Vikingur (Faroe Isles) v Trepca ’89 (Kosovo)
Hibernians (Malta) v Tallinn (Estonia)
Alashkert (Armenia) v Santa Coloma (Andorra)
The New Saints v Europa (Gibraltar)
Linfield v SP La Fiorita (San Marino)
Champions League second qualifying round
Apoel (Cyprus) v Dudelange (Luxembourg)
Zalgiris (Lithuania) v Ludogorets Razgrad (Bulgaria)
Qarabag (Azerbaijan) v Samtredia (Georgia)
Partizan (Serbia) v Budućnost Podgorica (Montenegro)
Hibernians (Malta) or FCI Tallinn (Estonia) v Salzburg (Austria)
Sheriff (Moldova) v Kukes (Albania)
Astana (Kazakhstan) v Spartaks Jurmala (Latvia)
BATE Borisov (Belarus) v Alashkert (Armenia) or FC Santa Coloma (Andorra)
Zilina (Slovakia) v Copenhagen (Denamrk)
Hapoel Beer-Sheva (Israel) v Budapest Honvéd (Hungary)
Rijeka (Croatia) v The New Saints or Europa (Gibraltar)
Malmo (Sweden) v Vardar (Macedonia)
Zrinjski (Bosnia and Herzegovina) v Maribor (Slovenia)
Dundalk (Ireland) v Rosenborg (Norway)
FH Hafnarfjördur (Iceland) v Víkingur (Faroe Islands) or Trepça ’89 (Kosovo)
Linfield or SP La Fiorita (San Marino) v Celtic
IFK Mariehamn (Finland) v Legia Warszawa (Poland)