Crusaders FC will being their 2013/14 European campaign against Champions League group stage regulars Rosenborg BK, from Norway.
The first qualifying round draw took place in Nyon on Monday, when Glentoran FC drew Icelandic team KR Reykjaviik.
Linfield are off to the Faroe Islands to play ÍF Fuglafjørdur.
All 38 first qualifying round ties are played on 4 and 11 July, with the reward for the winners a place in the second qualifying round on 18 and 25 July.
The tournament concludes with the final at the Juventus Stadium, Turin, on Wednesday 14 May.