Rangers will face Poland's Legia Warsaw or Atromitos of Greece in the Europa League play-off round if they defeat Denmark's Midtjylland.
Aberdeen's opposition if they overcome Croatia's Rijeka will come from Gent of Belgium or Larnaca of Cyprus.
Should Celtic lose to Cluj in Champions League's qualifying, they will drop into the Europa League play-offs.
Neil Lennon's side will face Moldava's Sheriff Tiraspol or Sweden's AIK if beaten by the Romanians.
Ties will be played on 22 and 29 August.
Rangers could have faced Wolverhampton Wanderers, PSV Eindhoven or Steau Bucharest in Monday's draw.
Aberdeen's potential opponents included Espanyol, Feyenoord and Sparta Prague.
Head coach: Aleksandar Vukovic, 39, is in his third spell as interim boss.
Last season: Second in Ekstraklasa.
European record: Beat Europa of Gibraltar and KuPS of Finland to reach third qualifying round but lost at that stage last season to Dudelange of Luxembourg.
Defeated Aberdeen in the Uefa Cup in 1990-91 and, more controversially, were knocked out of the Champions League qualifiers by Celtic in 2014 despite a 6-1 aggregate win because they fielded an ineligible player.
Notable players: Former Hearts winger Arvydas Novikovas signed from Jagiellonia Bialystok this summer, as did Serbia left-back Ivan Obradovic from Anderlecht, while centre-half Igor Lewczuk has returned after three seasons with Bordeaux.
Former Dundee United goalkeeper Radosław Cierzniak and striker Vamara Sanogo, who had a spell with Fleetwood Town, are also in the squad.
Head coach: Giannis Anastasiou, 46, a former Greece striker, took over in May after moving from Cypriot club Omonia.
Last season: Fourth in Greek Super League.
European record: Beat Danajska Streda of Serbia this season. Lost 2-1 to Newcastle United in the play-off round in 2012 and have reached that stage twice more since.
Notable players: Apostolos Vellios is a former Everton, Blackpool and Nottingham Forest striker. Goalkeeper Balazs Megyeri was a youth with Bristol City and had a spell with Olympiakos.
Head coach: Jess Thorup, 49, took over in 2018 after leaving Midtylland in his Danish homeland.
Last season: Finished fifth in Belgian First Division and were runners-up in Belgian Cup final, losing to Mechelen.
European record: Beat Viitorul Constanta of Romania to reach third qualifying round.
Notable players: Sweden right-back Mikael Lustig signed this summer after leaving Celtic, while striker Laurent Depoitre arrived from Huddersfield Town. Former Norwich City and Rotherham United midfielder Vadis Odjidja-Ofoe is also on the books.
Head coach: Imanol Idiakez, 47, appointed this year after being sacked by Spanish club Zaragoza in October.
Last season: Runners-up in Cypriot First Division.
European record: Have beaten Petrocub Hincesti of Moldova and Levski Sofia of Bulgaria this season. Reached the group stage last season, finishing third in their section.
Notable players: Former Zaragoza centre-half Mikel Gonzalez is among a group of seven Spaniards in the squad. Simranjit Thandi, a 19-year-old English defender, signed this summer from Stoke City.