Celtic was drawn against Sarajevo in the Champions League first qualifying round, while Rangers learnt its Europa League fate.
While Celtic completed a third straight domestic treble in 2018-19, it failed to reach the group stage of Europe's elite club competition after falling to AEK Athens in the third qualifying round.
Neil Lennon's team will begin its quest to return to the Champions League with a home match against Sarajevo on July 9 or 10, with the return game in Bosnia-Herzegovina taking place the following week.
"The biggest mistake you can make is underestimating a team like this. It's the Champions League so anything can happen. You just have to do your research and do as well as you can," said the club's on-loan attacker Daniel Arzani.
"I think we have the quality to go all the way. We just have to stick our heads down and get the job done."
Rangers will take on either Kosovan side Prishtina or St Joseph's of Gibraltar in the Europa League first qualifying round on July 11. The second leg will take place at Ibrox the following week.
Kilmarnock was pitted against Connah's Quay Nomads of Wales and Aberdeen drew Finnish side RoPS.
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