Shamrock Rovers will play Slovan Bratislava in the first qualifying round of the Champions League.
The League of Ireland champions will travel to Slovakia for the first leg on July 6/7 with the return game in Dublin on July 13/14.
Slovan beat Irish opposition in 2019 when they defeated Dundalk 4-1 on aggregate in Europa League qualifying.
Irish Premiership winners Linfield face Lithuanian side Zalgiris Vilnius while Wales' Connah's Quay Nomads will take on Armenian outfit Alashkert.
The draw for the second qualifying round takes place on Wednesday and features Celtic, whose potential opponents are Rapid Vienna, Galatasaray or Midtjylland.
The draw for the first qualifying round of the new Europa Conference League threw up several trips across the Irish Sea.
Welsh clubs Bala Town and The New Saints will face Larne and Glentoran respectively while Newtown will take on Dundalk.
Coleraine were drawn against Velez of Bosnia and Herzegovina while Bohemians and Sligo Rovers both face Icelandic opposition - Stjarnan and Hafnarfjordur respectively.
Hibernian and Aberdeen will find out their second qualifying round opponents on Wednesday.