Fenerbahce and Gornik Zabrze, Hearts’ possible opponents, finished as runners-up last season in Turkey and Poland respectively, with Jagiellonia Bialystok finishing behind the latter on goal difference.
Third-round qualifying ties in the Champions League are scheduled for 4/5 August and 11/12 August, with Europa League and Conference League games on 6 and 13 August. Dates and home-and-away details are yet to be confirmed.
Hearts, who play their first leg against Sturm in Graz on Tuesday, last took part in Champions League qualifying in 2006-07, when they were eliminated at the third qualifying round by AEK Athens.
Last term, Rangers started in Champions League qualifying and finished 32nd in the 36-team Europa League league phase after picking up just one win from eight games.