Craigan welcomes a British-based Europa League opponent
Motherwell will meet Llanelli in the first qualifying round of the Europa League, with the ties on 2 and 9 July.
Welsh side TNS face Fram from Iceland, while Northern Irish pair Linfield and Lisburn meet Randers of Denmark and Zestafoni of Georgia, respectively.
Scottish Cup runners-up Falkirk will play Vaduz of Liechtenstein at the second qualifying stage.
Welsh side Bangor meet Finnish outfit Honka and Northern Ireland's Crusaders face Macedonia's Rabotnicki.
The winner of Motherwell and Llanelli will take on Flamurtari Vlore (ties on 16 and 23 July).
The Albanian Cup winners famously defeated Barcelona 1-0 in a Uefa Cup tie on their home ground 12 years ago, only to lose the away leg 4-1.
The Steelmen will play their home legs at Airdrie's Excelsior Stadium since work is done on the Fir Park pitch, while Llanelli may move their home tie to the nearby Parc y Scarlets rugby ground.
"I'm delighted with the draw," said Motherwell chairman John Boyle.
"It takes a large part of the uncertainty out of the equation and it also suits the players.
"They are back to training early and so from a logistical view it's ideal although it's still going to be a tough game.
"But we will concentrate on the first round only. It's a bit previous to be deciding that you are going to go through. It's an old cliche I know, but we will take one round at a time."
Falkirk embark on their first ever European campaign against opponents who were relegated from the Swiss Super League last season.
In their only previous match against Scottish opposition Vaduz lost out to Livingston on the away goals rule in a Uefa Cup qualifier seven years ago.
The tournament replaces both the Intertoto Cup and the Uefa Cup, with three qualifying rounds and a play-off round being held before the group stages.
Aberdeen will be seeded for the third qualifying round draw on 17 July, along with English Premier League outfit Fulham.
Meanwhile, Aston Villa, Everton and Hearts enter at the next stage, the draw for which is on 7 August.
At that level 35 winners are joined in the final play-off round by another 41 clubs, including the 15 losing teams for the Champions League third qualifying round, on 20 and 27 August, for a place in the group stages.
From those ties, 38 winners will be joined by 10 losing sides from the Champions League play-off round in 12 groups of four teams.
After playing each other on a home and away basis, the top two teams in each of the 12 groups progress to the Round of 32, being joined by eight teams who finish third in their Champions League group.
The tournament then progresses to the Round of 16, quarter-finals and semi-finals.
Hamburg will host the final on 12 May.
First qualifying round
1 FC MTZ-RIPO Minsk (BLR) v FK Sutjeska (MNE) 2 FC Lahti (FIN) v KS Dinamo Tirana (ALB) 3 FK Vetra (LTU) v CS Grevenmacher (LUX) 4 Rosenborg BK (NOR) v NSI Runavík (ISL) 5 Haladas FC (HUN) v FC Irtysh Pavlodar (KAZ) 6 Sligo Rovers FC (IRL) v KS Vllaznia (ALB) 7 FC Olimpi Rustavi (GEO) v B36 Torshavn (FRO) 8 Anorthosis Famagusta FC (CYP) v UN Käerjéng 97 (LUX) 9 NK Slaven Koprivnica (CRO) v Birkirkara FC (MLT) 10 FC Zimbru Chisinau (MDA) v FC Okzheptes Kokshetau (KAZ) 11 Lisburn Distillery FC (NIR) v FC Zestafoni (GEO) 12 Helsingborgs IF (SWE) v FC MIKA (ARM) 13 Valletta FC (MLT) v Keflavik (ISL) 14 FC Dinaburg (LVA) v JK Nomme Kalju (EST) 15 FK Buducnost Podgorica (MNE) v KSP Polonia Warszawa (POL) 16 NK Rudar Velenje (SVN) v JK Trans Narva (EST) 17 Motherwell FC (SCO) v Llanelli AFC (WAL) 18 NK Siroki Brijeg (BIH) v FC Banants (ARM) 19 FC Spartak Trnava (SVK) v FC Inter Baki (AZE) 20 FC Dinamo Minsk (BLR) v FK Renova (MKD) 21 Randers FC (DEN) v Linfield FC (NIR) 22 Simurq PFC (AZE) v Bnei Yehuda Tel-Aviv FC (ISR) 23 The New Saints FC (WAL) v Fram Reykjavík (ISL)
Matches played on 2 and 9 July
Second qualifying round
Winners Match 4 v FK Qarabag (AZE) FC Pacos de Ferreira (POR) v Winners Match 10 Winners Match 15 v AC Juvenes-Dogana (SMR) SK Sturm Graz (AUT) v Winners Match 18 FC Basel 1893 (SUI) v FC Santa Coloma (AND) FC Honka Espoo (FIN) v Bangor City FC (WAL) MSK Zilina (SVK) v FC Dacia Chi?inau (MDA) Winners Match 8 v FK Petrovac (MNE) Saint Patrick's Athletic FC (IRL) v Winners Match 13 AC Omonia (CYP) v HB Torshavn (FRO) NK Gorica (SVN) v Winners Match 2 SK Sigma Olomouc (CZE) v Winners Match 23 Legia Warszawa (POL) v Winners Match 7 Falkirk FC (SCO) v FC Vaduz (LIE) IF Elfsborg (SWE) v Winners Match 5 SK Rapid Wien (AUT) v Winners Match 6 FC Naftan Novopolotsk (BLR) v KAA Gent (BEL) SK Liepajas Metalurgs (LVA) v FC Dinamo Tbilisi (GEO) FC Differdange 03 (LUX) v HNK Rijeka (CRO) FK Suduva (LTU) v Winners Match 21 Winners Match 3 v HJK Helsinki (FIN) FK Milano (MKD) v Winners Match 9 Winners Match 20 v Tromso IL (NOR) KR Reykjavik (ISL) v Larissa FC (GRE) Brondby IF (DEN) v FC Flora (EST) Aalborg BK (DEN) v FK Slavija Sarajevo (BIH) FC Steaua Bucuresti (ROU) v Ujpest FC (HUN) FC Metalurh Donetsk (UKR) v Winners Match 1 FK Rabotnicki (MKD) v Crusaders FC (NIR) Winners Match 22 v Winners Match 14 NAC Breda (NED) v FC Gandzasar Kapan (ARM) PFC Cherno More Varna (BUL) v FC Iskra-Stali (MDA) FBK Kaunas (LTU) v FK Sevojno (SRB) KS Flamurtari (ALB) v Winners Match 17 Winners Match 11 v Winners Match 12 Skonto FC (LVA) v Derry City FC (IRL) Sliema Wanderers FC (MLT) v Maccabi Netanya FC (ISR) FC Tobol Kostanay (KAZ) v Galatasaray AS (TUR) Winners Match 16 v FK Crvena Zvezda (SRB) FK Sarajevo (BIH) v Winners Match 19
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