Bohemians have drawn Levadia Tallinn of Estonia in the UEFA Cup qualifying round while FAI Cup holders Longford Town will face Vaduz of Liechtenstein.
Meanwhile Irish league side Glentoran will face Allianssi of Finland while Portadown face Zalgiris of Lithuania.
There were 50 clubs in the hat for this round, divided into three geographical seeding groups.
The 25 winners from the first qualifying round will progress to the second qualifying round, where they will be joined by a further 39 clubs.
The 32 survivors of the second qualifying round will progress to the first round proper, where 32 other clubs lie in wait.