The Dons face BK Häcken of Sweden while Hibs take on FC Santa Coloma of Andorra.
Should the Pittodrie side advance, Stephen Glass’ side will play the winners of the tie between Austria Wien and Icelandic outfit Breidablik, while Hibs face Malta’s Gżira United or HNK Rijeka of Croatia.
Elsewhere in the European draws, Rangers will take on Malmo or HJK Helsinki in their opening Champions League qualifier while Celtic face either PSV Eindhoven or Galatasaray if they reach the third qualifying round.
Steven Gerrard's seeded side were drawn out of the pot second and face a trip to Sweden or Finland for the first leg on August 3-4.
Malmo will host Helsinki - the former club of Gers striker Alfredo Morelos - in the first leg of the second qualifying round on Wednesday.
The Hoops are also due to be away for the first leg, if they can get past Denmark’s Midtjylland.
Ange Postecoglou kicks off his Celtic reign against the Danes at Parkhead on Tuesday.
Should the Hoops fail to progress past Midtjylland they face an encounter with Jablonec of the Czech Republic, with the first leg away from home.
St Johnstone will play the losers of the match beween PSV Eindhoven and Galatasaray in the Champions League in the third qualifying round of the Europa League.
Saints will be away from home in the first leg on August 5.