Kosovan side Prishtina will host their opponents from Gilbratar next Thursday in the first leg of their preliminary round clash. They will meet again the following Tuesday.
Kilmarnock will return to Europe for the first time in 18 years with a tie against Welsh side Connah's Quay Nomads. The Rugby Park club announced the hiring of new boss Angelo Alessio as the successor to Steve Clarke earlier this week.
Aberdeen, meanwhile, were drawn against RoPS Rovaniemi of Finland. The Dons have qualified for the Europa League in each of the last six seasons but have thus far failed to make it to the group stage.
The matches will be played on 12 and 19 of July. The second round draw will take place tomorrow.