Motherwell will start their quest for Europa League qualification next month against Iceland's Breidablik.
Craig Brown's side, who finished fifth in the Clydesdale Bank Premier League last season, will play the first leg of the match at Fir Park on July 15.
The return leg of the second qualifying round fixture will take place in Iceland on July 22.
Monday's draw also paired Airtricity League Sporting Fingal with Maritimo - with the first leg taking place on the Portuguese island of Madeira.
Irish compatriots Shamrock Rovers will play either FC Ulysses of Armenia or Israel's Bnei Yehuda in the second qualifying round, while Port Talbot will face Belgium's Cercle Bruges if the Welsh side win their double-header against Finland's TPS.
Principality Welsh Premier League rivals Bangor City have home advantage in the second leg of their second qualifying round tie against Finland's Honka.
In the first qualifying round, Llanelli were paired with Tauras on July 1, with the second leg in Lithuania the following week. The winners face Israel's APOEL. Portadown have been drawn at home to Latvian side Skonto in the first leg, with the team to progress facing either Qarabag (Azerbaijan) or Metalurg Skopje (Macedonia).
IFA Premiership rivals Glentoran have home advantage in the second leg of their game against Iceland's KR on July 8, with Karpaty of the Ukraine awaiting the winners.
Ireland's Dundalk will meet Luxembourg's Grevenmacher, with the opener taking place at Oriel Park and Levski Sofia of Bulgaria awaiting in the second qualifying round.
Liverpool, Manchester City, Aston Villa, Hibernian and Dundee United will not know their opponents until later in the summer.
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