Brendan Rodgers' side were drawn against Alashkert in the first qualifying round as they seek to reach the group stages for a third consecutive year.
Alashkert, who knocked St Johnstone out of the Europa League three seasons ago, are due to play at home in the Armenian capital Yerevan in the first leg, although selections are subject to change.
Celtic begin the first of what they hope are four qualifying rounds on July 10-11.
Northern Irish champions Crusaders were paired with Bulgarians Ludogorets, the highest-ranked team in the draw.
Ludogorets have twice reached the group stages in the past four seasons, playing Liverpool and Arsenal along the way.
The New Saints, who were seeded in the draw, will face Macedonian champions Shkendija.
Shkendija drew twice with Aberdeen in the Europa League three years ago, in their most recent European experience, with the Scots progressing on away goals.
Cork City were handed a tough encounter against Polish side Legia Warsaw, although they were given a boost when the losers of their tie were earmarked as automatic entrants to the third qualifying round of the Europa League.
The rest of the first-round losers will enter the second round of the Europa League qualifiers in a new champions path.